Supposing the character can speak in some sort of sign and isn't deaf, I'm not seeing anything in the spell discription that would prevent animals from understanding you. All it says is "You can comprehend and communicate with animals," and doesn't denote verbal communication. Well, then again there's the verbal component, but I'd say a character who somehow compensates for that would be able to.
Comprehend Languages by a strict reading of the RAW only allows you to understand the spoken words of creatures or read otherwise incomprehensible written messages," but to be honest I believe they just weren't thinking of signs when they wrote this. Similar with Tongues. (Tongues has the line "Tongues does not enable the subject to speak with creatures who don’t speak," but I believe this is meant mainly for animals, not mute humanoids.)
Stuff like Message and Whispering Wind would be a little trickier to justify, but personally I'd be willing to bend the "must whisper" requirement for non-deaf mutes when transmitting messages in a spoken language, since presumably they can understand a spoken language just fine -- plus a mute character who talks to others using spells or special abilities would be a cool concept.