How do you spell tear apart?

That is the correct spelling of "tear apart" (rip into pieces).

The verb "tear" has a homophone "tare" (the weight of an empty container)

The noun "tear" is a heterophone (teer), for a drop of liquid from the eye.

So:

Tear as in teardrops and tear as in tear apart, are spelled the same, but pronounced differently.

Tear as in drops is a noun (teer).

Tear as in apart is a verb (tayr).