Sometimes, it's tough to figure out where a title comes from. And then comes along a narrator like Manny, who tells us just what's up. Thanks, Manny.
According to Manny, the phrase "parrot in the oven" is actually a pretty common saying. So when his dad calls him "perico" (a.k.a. parrot), Manny knows that there's a story behind that nickname. Check it:
Perico, or parrot, was what Dad called me sometimes. It was from a Mexican saying about a parrot that complains how hot it is in the shade, while all along he's sitting inside an oven. […] I didn't mind it so much, actually, because Dad didn't say it because he thought I was dumb, but because I trusted everything too much, because I'd go right into the oven trusting people all the way—brains or no brains. (4.13)
So the idea of Manny being a parrot in the oven tells us that he's a seriously trusting guy. And it sounds like Dad thinks this is a bad quality. But since a parrot heading into an oven doesn't exactly sound like the bees knees either, this title gives us a little foreshadowing that Manny puts his trust in folks too much. Sometimes, he's going to be let down.
As for the mi vida component of the title, mi vida means my life in Spanish. This does two things: It lets us know that the story of Manny's life is about trust, and it also gives us a heads up that this book has one foot in two different languages and cultures.