Is there any way to fix or replace the mini USB port?

Yeah, I have an optional arrangement for you. But I would like to tell you that it may work if the USB is in the condition to follow these steps. You have to check whether your drive is spinning or not. If, yes, then take out the drive from the enclosed space and link it to the motherboard of your PC or you can also try it to install on other available USB jack. This will cancel your assurance period but ultimately you will find a way to get your data back. On the other hand, if you have RMA and return your drive, then surely your data will be vanished.

I hope this will work.

Good luck!