Aox is powerful, but not divine.
Think of it like this: The Gods operate on an entirely different mental paradigm than Mortals. Aox is powerful, but still a mere mortal. The staff compensates for his lack of understanding, but only so much.
A God can preform a complex rearrangement of molecules to turn a person into a frog. They can do this with out thinking about how they do it. A mere intuition. With but a thought they do this.
Aox would have to laboriously think through this entire process, carefully guiding power along the route. Even then he'd still harm the being in question.
It's like the difference between a normal person struggling through a complex mathematical equation, and a super-genius giving you the answer with but a glance.
Aox has more raw Oomph, but lacks this instinct and insight and wisdom.
“She'd become a governess. It was one of the few jobs a known lady could do. And she'd taken to it well. She'd sworn that if she did indeed ever find herself dancing on rooftops with chimney sweeps she'd beat herself to death with her own umbrella.”
― Hogfather