Learn Dutch: Het was de kunstenaar die weigerde, buiten dat hij boos was. - It was the artist who refused, besides the fact that he was angry.

The phrase buiten dat (besides the fact that) functions as a subordinating conjunction. In Dutch, subordinate clauses push the conjugated verb to the end of the clause. Therefore, was goes after boos.

Could I use behalve dat instead of buiten dat in this sentence?

Yes, they are interchangeable here. When used to add information (meaning "besides the fact that" or "apart from the fact that"), both buiten dat and behalve dat are perfectly fine. Note that behalve dat can also mean "except that" (introducing an exception rather than an addition), but context usually makes the intended meaning clear.

Since we are referring to a person, why use die instead of wie for "who"?

English speakers often want to translate "who" as wie. However, in Dutch relative clauses, you must use die to refer back to de-words (like de kunstenaar) and plurals, even when referring to people! Wie is generally only used for people after a preposition (for example, de kunstenaar met wie ik sprak - the artist with whom I spoke).

Why does the sentence start with Het was (It was) instead of Hij was (He was)?