Q: can't shut off bluetooth on mini

I would call Apple since it appears you have a defective Mini.

You have 90 days or free telephone support.

https://www.apple.com/support/complimentary/

YOu can also try this. If not successful then call Apple

- Try resetting the SMC and NVRAM/PRAM

Intel-based Macs: Resetting the System Management Controller (SMC)

https://support.apple.com/en-us/HT201295

About NVRAM and PRAM

https://support.apple.com/en-us/HT204063

- Try starting in Safe Mode

OS X: What is Safe Boot, Safe Mode?

https://support.apple.com/en-us/HT201262

- Boot to Recovery and repair the startup disk

OS X: About OS X Recovery - Apple Support

https://support.apple.com/en-us/HT201314

- If it is repairable reinstall the OSX

How to reinstall OS X on your Mac - Apple Support

https://support.apple.com/en-us/HT204904

- If you do not have a backup use disk utility to restore the internal disk to an external disk so you can try to recover data.

Then format the startup disk and do a fresh install of OSX

What keyboard and mouse are you trying to use...?

(brand name, model and are they new or used)

It could be that the Mac Mini's USB ports are bad. However a bad keyboard, mouse or USB cable would also cause a problem.

I would,

1. Disconnect everything including the power cord for a minute.

2. Re-connect the power cord.

3. Plugin the USB keyboard and mouse.

4. Then startup the Mac Mini.

If it does not see the USB keyboard and mouse then...?

I would,

1. Try a different USB keyboard and mouse.

2. Call Apple and/or return the Mac Mini.

FWIW: Bluetooth (ON) should not block you from connecting and using a good USB keyboard and mouse during the initial setup. The Bluetooth is only on by default, so the the computer can connect to bluetooth devices for the initial setup.

Good find, you're welcome!