What did you use to glue them together?
Super glue can be very brittle and has poor strength for larger parts that have a small gluing surface. You may be better off welding the parts together with a strong liquid glue.
As far as cutting delicate parts off the sprue, I found that it may help to cut the sprue itself around the part. While you do this, hold the part very close to where you are cutting so that it won't try to twist.
Once you get the part off the sprue "tree", carefully cut off the pieces of sprue that are still attached to the part. That puts less stress on the part itself and allows you to get the cutter at a better angle to the part. You may have to do this in a few steps, nibbling away at the pieces of the sprue on the part, until you finally get close to the part itself. Again, holding the part very close to where you are cutting. Finally clean up the part with an emory board or file.