As you probably guessed from the title, how would a mute person communicate? I know there's things like sign language or writing it out, but not everyone knows sign language, and you can't really have a conversation in real time by writing, unless you legibly scribble faster than the other person can read, and who can actually do that? So, taking that into account, how would someone without the ability to speak communicate with someone who can, but doesn't understand sign language and writing is not an option?
Human body language: Nods (yes), shakes (no), raised shoulders (don't know), blinks (play along/got it), moans (I'm in pain), grabbing (come with me), patting (pay attention), angry stare (I hate you), blank stare (don't bother me), smile (hello), frown (I'm sad), brush hair behind ear (like what I see), finger against throat (kill), hand in front of mouth (eat)... Wild language: Growl (stay away), bark (leave me), moan (I'm unhappy), sniff (hello there), lick (I like you), tilt head up (I submit to your will), stare (I dare you), show teeth (I'm ready to fight), bite neck (I'm the boss), drop dead animal (I want to be a part of your flock), eat first (I'm the alpha)...
I'd expect lots of facial expressions(smirks, eyerolls, raised eyebrows, grimaces) and lots of hand gestures/postures cues(shoulder shrugs, pointing, handroll, ect). But this will get tricky once it gets dark so it is harder to see, or with different cultures who have different meanings associated with the gestures. You could easily make it part of the characters development that they cannot understand each other at all when they first meet to being able to easily understand each other and get complex meanings from a few gestures.
I agree with the sugesstion of fundamental body language. You could also pull out a book and point to words. Or communicating through music/sounds made by other objects may also help.