iPhone 12 Mini unresponsive touchscreen

Make sure that you have updated to iOS 14.2.1. That addressing touchscreen issues on the iPhone 12 Mini.

This is an issue that has plagued many new iPhone 12 mini devices.... it usually occurs if there is a case AND a screen protector on the device. Take one or the other away and the problem goes away. Some work arounds to this have been noted such as touch the ring around the camera on the back side while swiping up on the screen (this solution has worked well for me). Apple just released an IOS update (14.2.1) that addresses this issue as well.