=don't destroy it. it means don't fail on deal with something. for eg.:you are taking a exam,so your mom tells you"don't screw it up",means do well in your exam and don't fail on dealing with it

"Don't screw it up" basically means don't mess up/don't destroy it. It also depends on how you use it in a sentence. example: "I'm counting on you to drive your sister to the mall today. Your father just washed the car. Don't screw it up." OR "This is a painting my mother did when she was a child. It is very special to me. Hang it up and DON'T screw it up" Alternatively, you can say just "don't screw up." example: "You only have a month left until summer vacation. Don't screw up and start missing a lot of days, or you'll be in summer school." OR "Don't get nervous on your road test and screw up." I hope that helped.

usually means do it well.