I picked up the same bad habit many decades ago.  I work on it every practice day, mostly by telling myself to 'relax, relax, relax.'  That includes trying to press on the fretboard as lightly as I can while still getting a clear note(s) and ensuring that all of my body is relaxed; arms, neck, shoulders, gritting teeth, etc..  I think proper posture and guitar position plays a role too.  In my case, an 'inexpensive' guitar at the very beginning of my journey was a nasty one to play and was probably at the root of my problem. Things improved when I went electric.  A better set up or even an 'easier' guitar might bring some positive results for you, too.  But now I have a trio of high-quality guitars and still lapse into the death grip from time to time.  It's a bad habit that's hard to break.

The tension/tight grip is troublesome, wrong, and gets in the way of improvement and speed.  Hopefully some instructors and other pro's here will have some additional advice for both of us.

A very late edit:  A strap.  Alway use a strap.  It you're not using one now, do so.  It'll relieve the effort of holding the guitar with the fret hand.

john