Stencil masking, though I doubt it will be faster if you have more than one volume concurrently.

Another alternative is clipping planes in a shader. For 4 planes it shouldn't be a problem (clipping the volume to the planes), but you probably have to clip the 4 planes themselves to new vertices if the original volume has many planes and you need that new polygon to close the clipped volume.

EDIT:

I probably misunderstood.. perhaps you just want a fast way to calculate the clipped volume, I was thinking about drawing..

Oh you should have said you were doing bouyancy stuff earlier. Erin Catto has a very good article in Game Programming Gems on bouyancy + triangle clipping. The way it works requires no additional tools or authoring, and will work for triangle meshes (not necessarily convex).

I wrote a bit about it here, but be sure to also read his article (I think in programming gems 4, maybe 3): http://www.randygaul.net/2014/02/14/buoyancy-rigid-bodies-and-water-surface/

But you did say 4 planes. If you're doing bouyancy stuff, why 4 planes instead of just 1?