The majority of male mice in a Mexican village lament the fact that Speedy Gonzales has been getting in between them and the "pretty girls." One of the mice suggests that they get the "gringo pussycat" Sylvester to chase Speedy out of town. The mice forge a note from Speedy, stating that he will pull Sylvester's tail out by the roots, which Speedy happily does when confronted by the cat. In trying to get Speedy, Sylvester first uses a shotgun and then a hand grenade; with the usual disastrous results. Speedy, however, falls for the cat's final attempt: A wind-up doll. With Sylvester hot on his feet, Speedy grabs the wind-up toy, and takes refuge in a box of red hot peppers; forcing the hungry pussycat to swallow them one by one in order to find the resourceful rodent. In between each ingestion of pepper, Sylvester runs to a nearby water cooler for relief. On his last trip to the cooler, he fails to notice that he's drinking out of a similar cooler filled with tabasco sauce; which sends the cat high into the horizon.
When this cartoon aired on Nickelodeon, a rather innocuous part where Sylvester says, "I'll get you if I have to eat every one of these things" as he is trying to find Speedy Gonzales in a box of chili peppers was cut. This scene is also cut on the Polish TV station Canal + Poland (evidence in here: http://chomikuj.pl/marciocha2504/CANAL*2b/Wrogowie+Gonzalesa,3678856645.avi(video)) This short on some TV prints has the 1957-59 Looney Tunes ending title card replaced with 1959-64 Merrie Melodies one.
On CBS, the two times Sylvester gets blown up (by a disembodied bullet and a hand grenade, respectively) were cut to remove Sylvester's appearance after the smoke clears.
This cartoon prompted Cartoon Network to keep Speedy Gonzales cartoons out of rotation in the United States due to their stereotypical depictions of Mexicans, though most Hispanic fans protested that Speedy Gonzales was not a stereotype. In Cartoon Network's final days of airing classic cartoons (between 2003 and 2005), some Speedy Gonzales cartoons did crop up on the network (mostly the late-1950s ones and a few from the post-1964 era), though not this one.