The Mute can be set at the switch (left hand) or automated when the CB breaks squelch.
HOw's the "feel" of your Mute switch in the left hand control? It should feel similar to the Cruise master switch with strong spring and good detents to push-on & push-off. If the feel is bad, and certainly a good place to start anyway, it'd be wise to clean that switch to ensure that it's opening all the way. Contacts that ar not seperating well in the Mute switch can cause the symptom you report.
The next place to look (easier) is the connections and radio ground, Pop up your center radio console (AM/FM/Cassette) and ensure that the connections to the back of the set are all tight - Removing the connectors and plugging them back in can dislodge any contaminants and also assure that you're "fully plugged-in" under there. One ground wire should be screwed to one of the 4 radio mounting botls - not often an issue, but a good time to double-check.
After that, you'll be hunting for a wire grounding when it shouldn't (hunt is on)... Of course, this is all predicated on the assumption that you're CB (if equipped) is off and not braking squelch and that you're experiencing this "mute" in both headset and speaker operation.