The combination of applying force with the knife edge while smacking the case at the seam will open it all the way around. You can see that by looking at it. The pack will look bumpy, not smooth. When it starts turning more freely, stick it in a player and wind it to the end, then back all the way to the beginning to repack it. It should then work normally again.
Cassette tapes are most difficult to splice because they're so small.
If the tape is damaged, you may have no choice but to edit out the bad area. Be aware that audio tapes are not as critical as video tapes as far as wrinkles going over the heads. If you only want it to last long enough to dub it over, go ahead and use scotch tape. Trim the broken tape ends if necessary to make a neat splice. If you're not using a splicing block, make sure the tape is straight when the splice is done.