You're actually not meant to fight the Nibble Mice (despite the fact that the game weirdly lets you.) You have to craft traps out of wood and metal. I can't remember where I got the blueprint for them though.
Where did you even find the hammer?
uh, it's like, the starting weapon? At least it's the one I started with on my save, it's the one I use to craft things. I realize now it functions more like a tool than a weapon so perhaps hitting the mice doesn't do enough damage. Also, so far I found stone and wood (from the baobab) but I have yet to encounter any metal. Do the gems count as metal?