How do I fix drywall that's separating in the corner?
 

Square room has one corner that is separating. The split is about 1/4" wide. Should I just caulk or remove original tape and retape/spackle/sand and paint?

Retape, mud it, sand, prime, and paint.

Do you have any idea when it began separating? You don't want to fix it, then have it come apart again because there is some issue with part of the foundation settling/sinking near that corner... or termite damage allowing a floor to drop.

Is it near an outside wall?

Agreed, unless it's new construction and the studs are still drying.