I don't want ios 8 on my ipad mini running ios 6. Is there a way that I can update to ios 7?
No, you can't do that. Apple only allows users to update to the latest software, as it fights version fragmentation. I recommend just updating to iOS 8.4.1. For the most part, whatever bugs existed in iOS 8 are fixed by now. You could also just wait until iOS 9 comes out in a couple of weeks, bug fixes and performance enhancements will be a major part of iOS 9.

This all is an effect of "code signing" where you need Apple to sign the version of code at the moment it gets installed. Since Apple no longer signs iOS 7 on that device, you would need to jailbreak or bypass that entire process.

Unless you're into the details of Jailbreaking you can stay at iOS 6 or upgrade to the versions Apple supports/signs.

I strongly recommend against jailbreaking, though.