Safety and quality of low-price imported beef sold in US supermarkets
Exporting meat into the United States is not a simple or easy matter.
From the United States Department of Agriculture (USDA) Food Safety and Inspection Service (FSIS):

Checklist for Importing Meat, Poultry and Processed Egg Products
This checklist is provided as an overview of the steps needed to be taken when you want to import meat, poultry, or processed egg products to the United States.

Products must originate from certified countries and establishments eligible to export to the United States.
The Animal and Plant Health Inspection Services (APHIS) restricts some products from entering the United States because of animal disease conditions in the country of origin. For information on restrictions related to animal diseases and information about APHIS, contact the APHIS Veterinary Services, National Center for Import and Export.
Countries and establishments become eligible following an equivalence determination process by FSIS.
Imported products must meet the same labeling requirements as domestically-produced products.
After filing the necessary forms for U.S. Customs and Border Protection, and meeting animal disease requirements of APHIS, all imported meat, poultry and processed egg products must be presented for inspection by FSIS at an official import establishment.


Mexico is one of 33 countries that can legally export meat to the US. In Mexico there are 74 companies authorized to export to the US (As of May 3, 2017).
USDA Source
Also from the USDA Website:

So, in the United States, beef from Mexico has been determined by the US Government to be as safe as domestic beef.