When a cat is stuck with mouse glue, you may want to try cleaning it first. If you cannot clean up the glue, you may consider removing the glued hair. Trim it off. If you are afraid that it will cause the cat to catch cold, you may want to put the cat in small clothes. If you don't want to shave off your cat's hair or if it sticks to the skin, you can scrub it with cooking oil to emulsify it and wipe it off, but be careful not to let the cat eat the oil when using it.