Hmmm yes and no, because generally we use the verb "improve" instead of "make better". So we would say "Reading can improve your mind". Or more idiomatically: "Reading can sharpen your mind".

The sentence is fine but not necessarily true.

Nothing wrong grammatically speaking, but it's better to say “improve our mind.” (I'm curious though. Are you talking about improving thinking skills or general knowledge? Putting those in might be even better.)