New Spain’s Quidditch team were finalists in the 1809 Quidditch World Cup, a disaster more commonly referred to as “The Attack of the Killer Forest“. While New Spain were ahead of them on points, Niko Nenad, a member of the Romanian team, hit a Bludger into the nearby Siberian forest, which he had enchanted to rise up and march against the players and crowd (Pm).
While New Spain, the core of which became Mexico after 1821, fielded a Quidditch team in the 1809 Quidditch World Cup final, there are no Quidditch or other wizarding sports teams listed in its Wikipedia entry (Wikipedia) or in the entry for its successor, Mexico (Wikipedia).
It is not specified whether the modern teams have also renamed themselves to the Mexican National Teams.
From the Web
Writing by J.K. Rowling on Pottermore:
Pottermore enhanced reading experience: Quidditch World Cup
Screenshots of the original Daily Prophet coverage of the 2014 Quidditch World Cup on Pottermore: Imgur web archive
Harry Potter Wiki: Mexican National Quidditch Team