So far it seems all these answers rest on misunderstandings of relativity
Relativity does not actually preclude objects moving faster than light, only objects travelling at the speed of light. As such, relativity prohibits objects accelerating from sublight speeds to superluminal speeds, but if we wave our hands around when we break the light barrier, and only consider the object once we already have it travelling faster than light we get pretty reasonable physics out again
A few starting points (working in natural units where c = 1):
The energy of a relativistic object (including its rest energy, which is just m) is:

The momentum of a relativistic object is:

Because both of these equations feature a factor of
you will sometimes see a concept of "relativistic mass" invoked, which is equal to this factor. Such a concept is generally considered deprecated in physics these days, because as soon as you start doing anything more complex than basic kinematics, it starts making things more complicated rather than less, and leads to some unhelpful intuitions
As an object approaches the speed of light (from either direction),
and so both
. This is known in the business as a Bad Thing, and means something unphysical is happening. This is why relativity predicts no objects can cross the lightspeed barrier. Luckily for us, the spear is made of handwavium and has a way around this
Unfortunately now we have a different problem. Because we now have v > 1,
is imaginary. In order for a bunch of other physics to make sense, we need Energy to be a positive real number, and so any tachyons in the universe (including our spear) must have negative imaginary mass, so the factors of i & -i in
cancel out
Again though, our spear is made of handwavium, and so as part of crossing the lightspeed barrier, its mass becomes negative and imaginary
Now we have a spear travelling at faster than light speed. The first thing to note is that it will emit gravitational Cherenkov Radiation. Cherenkov Radiation is normally encountered around nuclear reactors and is why they seem to glow blue, and is roughly the electromagnetic equivalent of a sonic boom. The normal sort is electromagnetic and occurs when a charged object travels through a medium faster than the speed of light in that medium. Gravitational Cherenkov Radiation is the equivalent with gravitational waves instead of electromagnetic waves, and will occur whenever a massive (gravitationally charged) object travels faster than speed of gravity in that medium (as we are in space, this is just the speed of light here)
As such, our spear will be emitting a bunch of weird, high energy gravitational waves, causing it to rapidly lose energy
Looking at the equation above for energy, and ignoring the pesky imaginary factors that we're cancelling with our handwavium, we see that whereas we're normally used to energy increasing as you speed up, energy actually increases as you get nearer the speed of light. As such, superluminal objects lose energy by accelerating, and so, as our spear loses energy by Cherenkov radiation, it accelerates. As this causes it to move at an even greater speed, it starts to lose energy even faster, and its speed rapidly heads towards infinity, and its energy heads back down to its rest energy m
Now this is where it gets interesting. From quantum mechanics, we know that the wavevector (essentially a vector consisting of the wavelengths in each direction, with a slightly different normalisation), and substituting our expression above for the momentum p:

As v > infinity, this goes to 0 in all directions
The reason this is interesting, is that from studying interactions in particle physics, we know that a particle will only interact with an object if it's wavevector is of a similar scale to that of the object. As the wavevector rapidly goes to 0, and any real object has non-zero size, the probability of the spear interacting also goes to 0
So where does that leave us?
The spear itself is not the danger, as the probability of it interacting will be essentially 0 shortly after it breaking the lightspeed barrier
What is dangerous though is the burst of Gravitational Cherenkov Radiation. This circular blast wave (perpendicular to the velocity of the spear) centred on the point at which the spear crossed the lightspeed barrier will carry almost all of the energy that went into accelerating the spear. Depending on how much of the crossover the handwavium applies to, this could be an astronomical amount
So, the spear allows you to concentrate the energy you build up propelling the spear into a circular blast wave where it breaks the lightspeed barrier. With a long enough run up, that's a lot of energy in a very concentrated burst and, because it's gravitational radiation, won't be able to be effectively blocked in the same way electomagnetic radiation might be able to. As such, it will get around shields, or physical armour. The downside is that gravity is comparatively weak and so you'll need to put more energy in the burst to do the same damage