Disregarding the mass/energy issue (where a wormhole weighs an insane amount). We'll just assume that the physical essence (the wormhole itself) of the wormhole has no effect on the universe other then allowing 2 distant places to be linked together.
My first thought was something like a giant vacuum cleaner.
In particular, we'll say that one mouth is floating somewhere in free space, and the other falls into Earth's gravity well. The radius of the mouths is 1 meter.
Where the atmosphere blasts out of the end of the worm hole into space. But after thinking about this for some time. I realize that earths gravity may well transverse the wormhole too. So you may get some atmosphere shooting into space, but it could form a spherical ball around the wormhole (Assuming the wormhole is spherical in effect). Held there by earths gravity, at some point these two forces would probably equalize.
If the wormhole hit[was on] the ground, I doubt anything special would happen. I don't think much dirt and rock would get sucked out into the void just by the shear vacuum of space. Again, because earth has enaugh gravity to hold this stuff normally and just a 1 meter area of vacuum probably wont overcome that.
So if you allow the vacuum of space to transverse the wormhole, you almost have to allow gravity and anything else to transfer too.
Some of this depends on how you define
other falls into Earth's gravity well
If you mean in orbit, this may not do anything. It's not like you can drain the gravity of the planet away. It might create a navigational hazard. At worst you would get a area on the opposite side of the wormhole that has a bit less gravity, like a stone in a river slows the river just behind the stone. This wouldmay be less noticeable the further away from the wormhole you go or there may be "hole" in earths gravity well where it's leaking though the worm hole.
Of course you could have a one way wormhole, I suppose.