Athletic director Chris Massaro said Wednesday in a statement that the actions captured in the video were disturbing.
Coach Rick Stockstill suspended the players until the investigation is completed, and Massaro says Akin and Alvarez will perform community service for local animal welfare groups.
The Daily News Journal first reported the investigation and suspensions. Murfreesboro detectives were contacted April 6 by someone who had seen video on Akins' Snapchat account showing Alvarez hitting a puppy four times.
Akins is a redshirt senior who played 13 games last season with 27 tackles, and Alvarez joined the team last year.