Chopping up an Animation

I need to divide a long animation into several smaller ones for use in a game engine. But if I delete the keyframes, it loses the influence of the keys that I deleted and accelerates from 0 instead of doing a hard cut. Of course, that’s what it’s supposed to do, but kind of bad in this scenario. How do I chop up an animation while keeping the influence of the keys that were deleted?

Normally the very first key frame defines the initial state of rig. So if you pull out key frames from mid sequence, the first key frame in that sequence needs a starting definition for the other key frame to follow. You need to redefine the first key frame.