Enmudece comes from the verb enmudecer, meaning 'to silence' or 'to make speechless'. It's a strong and evocative word that goes beyond simply 'not speaking'.
In the song, the singer uses it to describe how his
Have you ever felt so overwhelmed by fear that you just can't speak? That's exactly what Banda El Recodo De Cruz Lizárraga and Carlos Rivera sing about in "Maldito Miedo"! Our singer is totally stuck, saying "Otra vez el miedo me tiene vencido" [Again, fear has me defeated]. He's suffering from the same problem again and feels like a coward, even though he knows he isn't usually like this. He can't even speak when he wants to talk to this person!
It's a real battle in his head because he gets brave, but then something always stops him. He's so close to shouting "que la quiero" [that I love her], feeling like he'll die if he doesn't. But then that "maldito miedo" [darn fear] silences him, telling him not to open his heart because he might lose her. It's such a relatable feeling when you're on the verge of confessing your feelings, but fear just takes over!