He broke the mirror because it didn't work. He was in grief, and thought he had chance to see Sirius again. when it didn't work; he snapped, and broke it.
Kind of like how Sirius and Lupin tried to tell Harry that his father was simply immature, and not a bad man. What they all failed to realize is that while Harry is also 15, James never went through the horrors Harry has.
I hope in a future book Harry will see his father grow up into a kind and loving man, with Lily loving that man - not the one who showed off to get her attention.