I've had three tendons reattached after craft knife accident. (All at the same time, I'm not that clumsy.) They pull the ends together and sew with dissolving thread or staple like any other tissue, then close over the top. I'm told this is significantly easier if the tendon is cleanly severed with a sharp knife than if it snapped from over stressing, because they don't have to worry about the stitches pulling out through weak points in an uneven tear, or about lining the ends up just so.

A friend has had laparoscopic surgery on a tendon to remove a frayed edge that was rubbing against other tissue and causing pain. The surgeon cut two tiny holes, put a mini camera in one and a sharp snipper in the other, and snipped away the frayed part.