Entorpecen comes from the verb entorpecer, meaning to make clumsy, hinder, or slow down. It's a less common but very descriptive word.
In the song, the singer uses it to express how his lips "become clumsy" or "are hindered" when the woman of his dreams appears, making him unable to speak. This vividly captures the feeling of being so overwhelmed by someone's presence that you lose your words.
Have you ever been so smitten you can barely speak? That's exactly what Los Rumberos and Alex Cuba are singing about in "Riéndose de Mí" [Laughing at Me]. Our singer is completely captivated by the "señora de mis sueños" [lady of my dreams], but every time he tries to talk to her, his "boca no lo sabe decir" [mouth doesn't know how to say it]. His lips get tangled, and his reason just flies away!
He imagines kissing "cada rincón de tu cuerpo" [every corner of your body] to make the night's suffering disappear. He promises he could make her happy in an instant and playfully suggests, "si crees que soy un niño te nombro mi muñeca juguemos a dejar de fingir" [if you think I'm a child, I'll call you my doll, let's stop pretending]. He's taken a risk coming to her, driven by love, and he's determined to find a way to make her fall in love with him. He sees her body as a "monumento" [monument] and just wants to get closer.