How can I delete pictures on my iPad mini without them being deleted on my other devices as well? If I delete a picture on my iPad mini, it also deletes that picture on my iPhone too. I want to remove a lot of photos on my iPad mini and only my iPad mini.
Unfortunately, you can not. Because you have iCloud Photo Library turned on, all of your devices' camera rolls are identical. Apple's thing about iCloud Photo Library is that everything is perfectly in sync, there's no photo you have on one device and not the other.

You could consider turning iCloud Photo Library off and deleting all the stored photos (in Settings > iCloud > Storage > Manage Storage > iCloud Photo Library, then select Disable and Delete) but that will cause problems potentially including a loss of photos. Be sure to back up all of your photos to Google Photos/a hard drive before attempting to turn off iCloud Photo Library.



Freeing up space

My guess is that you want to delete photos from your iPad Mini to free up storage space on your iPad. You can go about this even without deleting your iCloud Photo Library.

Turning off iCloud Photo Library on only your iPad Mini:

From Apple:


  You can turn off iCloud Photo Library on a single device when you follow these steps:
  On your iPhone, iPad, or iPod touch, go to Settings > iCloud > Photos and turn off iCloud Photo Library.


This will delete your photos from your iPad but not your iPhone or iCloud account.

Then, you can back up your photos with Google Photos: download the Google Photos app on your iPhone, let it back up all of your photos from your iPhone (this won't eat into your Google Drive storage space at all and is totally free), then download the Google Photos app to your iPad. Now, you can view all of your iPhone's photos right on your iPad and they won't eat into your iPad's storage space.