Mutante literally translates to "mutant," but in this context, it's used to mean 'changing' or 'unstable'. It's a very striking and modern word to describe a feeling.
In the song, the phrase "amor mutante" (mutant love) powerfully conveys a relationship that is inconsistent and unpredictable. This isn't a steady, reliable love; it's one that transforms and changes its form, making it a perfect word for a complex, modern romance.
Mexican rock band Maná really knows how to write a messy, addictive love drama. In Labios Compartidos, the singer is totally hooked on someone who treats him like a part-time option. He admits it straight out: she uses him up and tosses him aside (me tomas, me dejas, me exprimes y me tiras a un lado [you take me, you leave me, you squeeze me dry and throw me aside]), leaving him waiting like a faithful stray (me tienes como un perro a tus pies [you have me like a dog at your feet]). Then she flutters off to other lovers like a hummingbird (como los colibrís). It is dramatic, a little humiliating, and painfully honest about being trapped under someone else's spell.
He calls the whole setup amigos con derecho [friends with benefits, literally 'friends with rights'], but complains he never gets the right to keep her full-time. Instead, he drinks under flashing lightning (relámpagos de alcohol) and waits around for his little ration of her attention: el pedazo que me toca de ti [the slice of you that falls to me]. He swears he cannot take sharing her kisses anymore (yo no puedo compartir tus labios), yet the chorus tells on him immediately. He still loves her without limits, even while split across other partners, because her lips are the ones calling all the shots.