A thin nail that bends when punched and snaps when pried can be pulled clean: set a washer over the exit point, grip the nail's tip in a rivet gun like a rivet mandrel, and squeeze — the nail draws straight through, intact.
Tear-out happens when wood fibers have no support behind the cut, so they break away instead of shearing. Either relieve the far corner first so your cut meets a shoulder, or clamp a backer block tight against the exit side.