EDIT: The question was edited and it shifted the context. I'm leaving my original answer for fun and giggles (everything below the line), but here's the new answer:
Gravity causes pressure
Gravity doesn't change mass (I'm ignoring things like enough mass leads to enough weight that things fuse and begin to burn... too complex for the example) — but it does change weight. As you add mass the available gravity increases which increases weight. The consequence is the creation of pressure.
However, it's unlikely (though we don't actually know from empirical evidene) that gravity is uniform from the center to the surface. The shell theorem mathematically proves that inside a hollow shell there is no gravity, the distant but more massive portions of the shell countering the gravitic pull of the mass behind you at any point in the shell.
Thus, as you descend toward the center, you only have the gravity of the mass below you to contend with until you get to the center where there is no mass below you and there is no gravity.
Which, curiously, suggests that the center of a supermassive black hole has no gravity, but that's an attribute for another question.
But pressure increases... odd that
Miners have long known that pressure increases as you descend into the earth. At first that seems counter-intuitive to what I just described since, theoretically, only the mass below you is affecting you.
But it's affecting the shell above you, too. And as that shell gets thicker, its weight changes. This is the cool part. In the beginning (methinks), gravity is growing smaller very slowly, but weight is increasing very rapidly, and thus so is pressure.
But, as you get near the center, the pressure toward the center must decrease because gravity (toward the center) has reduced so much that eventually there is no pressure at all.
Toward the center.
Now all the pressure is toward the surface. Using our tried and true "circular horse" method of modeling, it suggests that a homogenous mass will have a boundary (today, because I don't know if anyone has theorized this before — and I could be completely wrong — and they probably have so let me know so I can give credit where credit's due — but today, let's call it the "JBH critical pressure boundary." I'll reveal my true name when I publish....) where the pressure is at its maximum. The pressure from that infinitely thin shell within the volume of the sphere drops to zero as you descend toward the center or as you ascend away from the center to the surface (remember, homogenious mass... on a planet the outer zero-point would be somwhere above the "surface" in or near the surface of the atmosphere, yeah... non linear... cool!).
So, "boom!" has some cool effects
I'm lousy at art, even though a picture here would be worth a thousand words. But, let's say SomeGuy pulls the trigger on that bad boy weapon of his except rather than his cylinder, all gravity in the universe is instantly reduced to zero (this is important for the example, I'll explain in a moment).
You'd get a boom! A really cool boom! Because all mass below the "JBH critical pressure boundary" (TM until proven otherwise!) springs toward the center of the sphere until the pressure reaches a maximum against the nuclear bonds of the material of the mass and then rebounds away from the center.
The mass above the "JBH Critical Pressure Boundary" (look, caps, I'm making it official, remember you heard about it first (maybe) here folks!) simply springs away from the center. In both cases we're dealing with a spring effect. That mass begins oscillating as it compresses (for example) in the direction away from the centr, forcing the mass "above" (away from the center) to spring forward at increased speed.
So, in keeping with our spherical horse simplicity, your explosion has a whole series of "shock waves" comprised of the mass of the black hole. A really big shell of rapidly expanding matter followed by a small shell. I'll leave it to mathematicians to explain how far apart they are. Just expect to be slapped hard a whole bunch of times.
And they stay that way forever, or until you turn the gravity back on
And this goes on and on and on... Heck we're affecting the entire universe (here's that "explain in a moment" moment), so every glob of mass is doing the same thing. It continues to redistribute until shockwaves hit one another and then the biggest game of billiards the universe has ever seen begins. But that might not be interesting.
But, what if we can only affect a limited area?
Let's assume the weapon wasn't quite that godlike, but affected an area, say, twice the diameter of the event horizon. All this mass expands to that point and then begins to re-experience gravity. So it begins to re-coalesce in directions along the plane of the expanding shells, but not toward the center (Shell Theorem). It's very likely that the mass wasn't homegeneous, meaning there's variations of density within the shell, which means new globs are forming.
At this point, let's turn the weapon off.
Would the black hole reform? That would need a ton of math that's beyond my abilities to prove. The force of gravity (which isn't that strong "locally" for each glob) must overcome the velocity (kinetic energy) of the expanding particles. If the expansion was slow enough, it would reform ... eventually.
If fast enough it never reforms. It would take the galaxy time to realize that because from its perspective (a massively large ring while the expanding shell still looks like a small point) all that gravity is still there. I suspect that as the expanding shell passes star systems that it then raises massive havoc with those systems, which are suddenly inside the shell (Shell Theorem) and their trajectories are massively modified.
But they also receive a massive infusion of, well, mass. And that's cool becaues the shockwaves may be traveling fast enough to do this quickly, either pummeling planets into dust or layering mass just on one side causing serious rotational wobble. Heh heh heh...
After a while all stars will be affected as the shell grows larger and larger and must be dealt with, not as an infinetly small point at the center, but an ever larger plane that's much closer but much weaker.
It's catastrophic, kinda, but it wouldn't destroy the galaxy per-se because in all this time the mass has been forming, shifting, trading alliances...
Let the math prove me right or wrong, but I suspect given enough time a new supermassive black hole would form, but it wouldn't be in the same place. Some of the mass escapes the galaxy altogether, meaning all the dynamics will change at least some. Maybe a few of the outer stars (like Earth... Aaaahhhhhh!) spin off as rogue systems into intergalactic space. The time-lapse photography would be cool to watch.
Finally, the cylindrical "beam" of the OP's weapon...
In the condition that gravity can reassert itself so quickly due to the spatially small area effect of the weapon, there would be a boom, a whomping big boom, but reaserted gravity would begin to recoalesce the mass almost instantly. The black hole would take forever and a day to completely reform, but from the perspective of the galaxy, all that mass is still at the center, so it wouldn't notice a thing. The minor fluctuations in gravity caused by the actual shift in density during the explosive and recoalescing process might cause some of the nearby stellar systems to burp a bit, but those near the rim would be unlikely to feel anything at all (only detectable via instrumentation).
At least that's what I think'll happen...
This is the original answer to the original question, left only for historical purposes.
Newton's Third Law — for every action there is an equal and opposite reaction.
Which is a fancy way of saying if something's coming at you at 100 Newtons/s, the only way to bring it to a stop is to apply 100 Newtons/s in the opposite direction.
The answer, therefore, is no. It's not plausible. The force representing the black hole's gravity must go somewhere, and where it's going to go is the weapon. Thanks to gravity being more comprehensible as something that pulls you toward it, you'd "pull" against the black hole and the black hole would "pull" back.
This is an issue because gravity is a force that can actually push. It's not like lights where most of the energy is (or can be thought of as) heat. That's why lasers of tremendous melting capacity don't have a recoil.
But gravity recoils.
I'm a huge advocate of not getting too buried in the details. If what your weapon does is disrupt gravity or, perhaps more realistically (kinda), disrupts the nuclear bonds of the atoms comprising the black hole... then maybe you have an explanation that would make sense! Especially if you declare it to be independent of gravity so that whole "the black hole will just suck your beam in and consume it like everything else" problem.
I'd like to point out, though, that any civilization with the technology to destroy a black hole... especially one that can do so with a single weapon emplacement (the potential size is staggering)... is basically godlike. In such case, you don't really need to describe the how's. Just the why's.