As far as her being mute, she is not. If you can make growls, trills, hums, etc., you're using the vocal chords and thus could make the sounds of speech. (Technically, if your vocal chords were damaged, I figure you'd still be able to make kissing sounds, because those are from the lips and not diafram, but that doesn't matter since Paprika does more than kissing noises).
Regardless, she still may not be able to talk. Damage to Broca's Area (a portion of the brain responsible for speech) can cause speech impairments, but apparently it doesn't stop you from making other noises.
People will hate me for saying this, but it's also a possibility she is not mentally capable of speech, or never attempted to learn it due to disinterest. I'm no mental health expert, nor would I claim to be so, but she does seem to have some issues. If you read her Book of Lore chapter, you'll know that she has an ignorance of consequences or any situational gravity whatsoever, and fails at following basic instructions. Judging from her voice lines and animations while fighting, it's almost a given that she is completely unaware that there is a battle going on, despite being physically attacked. I honestly doubt she even understands that her tribe abandoned her.
Mind you, I'm not slating her intelligence. She can sew a mean sweater, so she is capable of fairly complex tasks. Clearly her brain is developed in terms of general intelligence. And I realize she's meant to be that cute funny character that everyone loves, and that I'm overanalyzing. But if you look at the facts, her behavior is indicative of a delusional mind, if not something more serious. If you're familiar with the Pyro from Team Fortress 2, she honestly reminds me of him. Ever since I started looking into her character, I've found her story to be the most sobering of the cast.