Yes, mute is a Scrabble word!
...and is worth 6 points in Scrabble, and 8 points in Words with Friends
mute
Verb
1. Deaden (a sound or noise), especially by wrapping
Adjective
1. Expressed without speech
2. Unable to speak because of hereditary deafness
Noun
1. A deaf person who is unable to speak
2. A device used to soften the tone of a musical instrument
What Scrabble words can I make with the letters in mute?
3 Letter Words
2 Letter Words