How you would avoid this for future reference, although I'm not sure if you did this prior to damage phase during attack. is not to hold priority after casting your first
mutagenic growth. You'd cast your first mutagenic, and give him priority. Then if your opponent casts his axe, you respond to it with the second growth. If he doesn't, then you just cast your next one.
This doesn't work if you're trying to do combat tricks and casting after blockers, but before damage. Because there won't be a second phase to cast a growth before the damage is declared.