When a particle collides with its antiparticle, they pair annihilate with emission of photon(s). What happens when a particle collides with an antiparticle that is not its own opposite? For example, what happens when a positron collides with a proton?

There's nothing magical about antimatter. It obeys the same physical laws as "ordinary" matter. It's just that the particles which make it up are "mirror images" of the particles which make up ordinary matter. And when a particle meets its "mirror image" - boom!

If a particle (ordinary or anti) collides with another particle (ordinary or anti), they undergo either scattering or fragmentation, unless they happen to be "mirror images" - that is, each other's antiparticles.

For more information, go to the Contemporary Physics Education Project.