Crudo literally means "raw" or "crude." However, in Mexican Spanish, it's a very common and colloquial term used to describe being "hungover."
In "Modo Crudo," Gerardo Ortiz uses this word to set the entire mood of the song. He sings, "Ando modo crudo / Con dolor de cabeza" (I'm in hangover mode / With a headache), immediately letting listeners know he's dealing with the aftermath of heavy drinking due to heartbreak. This double meaning makes it an interesting and culturally specific word to learn.
Gerardo Ortiz's "Modo Crudo" is all about that classic post-breakup coping mechanism: drinking your sorrows away! He's not even trying to hide it, admitting, "Otra vez te agarré de pretexto para emborracharme, y ¿qué?" [Once again, I used you as an excuse to get drunk, so what?]. He's fully aware that everyone knows his routine, saying, "Total ya me conocen y no es la primera vez que ando amanecido y digo que es tu culpa" [Everyone already knows me, and it's not the first time I've been up all night and said it's your fault].
He's in "modo crudo" [hangover mode], dealing with a headache and celebrating his sadness with multiple drinking sessions. He even jokes about his liver, thinking it can handle "otras veinte semanas pisteando y amaneciendo bien crudo" [another twenty weeks of drinking and waking up super hungover]. It's a blunt, almost darkly humorous look at how much he misses someone, and how he's dealing with that absence.