HenryIn generel: yes, you can. USB is independent of the connector type. But maybe you get in trouble with the case and the pcb because the connector has other measurements...
BTW.: why you want to do this?!
CodingDespite smaller size micro-USB is sturdier than mini-USB.
IIRC mini-USB socket was designed to survive minimum of 10k plug-unplug cycles, in case of micro-USB it is over 100k cycles.
In case of mini-USB most of wear and tear appears on socket, it is different in case of micro-USB, where the plug wears-off. It is much easier to replace cable than to replace socket.
Codingksmigrod already explained the most important reason. In addition to that I have a lot of micro USB cables lying around while I don't have any spare mini USB cables. In fact there's only single mini USB cable in my whole apartment and it is used for a scanner. However, I doubt I'd bother to replace the connector unless it breaks but if it does, it's going to become a micro USB connector.