Unfotunately, its not that simple.
To "Cut and Paste": there is only one crude method that actually works. (I never use it anymore though). btw this is for cutting and pasting from one anim to the next - you can already (as General Barron said) cut and paste in your own anim by using the "Frame Browser" Default key: F10
1. First, open up the anim you want to cut frames from. Open the Frame Broswer (F10)
2. Then select all the frames that you don't want to cut and delete them.
3. "Save Anim As" another name (so you don't alter the original - don't worry, this anim will only be temporary).
4. Now, you can either work around the frames you now have by inserting frames before and after the cut frames or you can procede to Step 5.
5. Here's where it gets messy (mainly cuase I don't really remeber what to do.
6. There's some sort of trick you can do with two OFPAnims open at the same time. You can move the the two anims to the same one and save it.