I am Mexican-American, and I don't consider the nickname "Mexi-cutioner" to be racist at all, and I will tell you why. Manny earned that nickname because the super lightweight division has historically been dominated by Mexican fighters, and Manny rose to fame off of his victories against the two elite Mexican fighters of his era - Barrera and Morales. Plus, Manny has openly expressed his admiration and respect for Mexican boxers and Mexican fight fans. Manny is actually quite famous among Mexican (note that I said Mexican, not Mexican-American) fans because of his aggressive, warrior-like style of fighting a la Julio Cesar Chavez.
However, I do understand why some take offense to this title. After all, as someone has pointed out already, if a white, Asian, or Latino boxer was nicknamed the "Blacks-a-cutioner" or the "Jew-cutioner", he would be immediately branded a racist. So I see where they are coming from. We live in a current society where anti-Mexican racism is widely prevalent, and Mexican culture/Mexican people are openly discriminated against because of backlashes against immigration, language policy, etc. I personally feel that in American society, people are far too tolerant of racism against the "new" minorities (Mexicans, Puerto Ricans, Asians, Arabs, Muslims, Indians) than they are against the "old" minorities (Blacks and Jews) because there is not the same level of guilt and repulsion at racism/prejudice against Mexicans or Asians as there is against anti-Semitism or anti-Black racism. I've expressed these views to various people - many people agree with me, but some have tried to defend this double standard on the grounds that, allegedly, Blacks and Jews have earned the right not to be discriminated against, while Latinos, Asians, and Arabs supposedly have not. I DO NOT agree with this thinking at all. If a person is considered a racist for using their political views on, say, affirmative action as a pretext for condemning and ridiculing Black people (for which, in fact, such a person would be a racist), then why is it socially acceptable for that same person to use their views on immigration as a pretext to condemn Mexicans?
We are either going to have a civil society that respects ALL people, or we are not. We can't have a two-tiered society that "red shirts" certain minority groups by declaring that they are "off limits" and cannot be touched, while at the same time it is considered "fair game" to go after other minority groups and openly insult them.