I built a separate structure on my property. It includes a studio space for my photography business. How do I deduct the building cost for this office space?

You can do either. 

If you choose to use it as a home office then you add the square footage of the new structure to the square footage of the other structure (your home) on your property in order to get the total square footage.  Then your home office deduction works as a percentage of the whole.

Or you can add up all of the costs associated with creating the new structure and call that "office space" and depreciate it as commercial real estate.  The costs will be recovered over a 39 year life.

Test it both ways and see what works for you.  If you were already depreciating your home office this would change that basis.

@lacyhaug