Mutt's Father is a Muttaburrasaurus, one of the species referred to as a Spikethumb by fans, who has only appeared in The Land Before Time III: The Time of the Great Giving. He is the father of Mutt.
It is likely that, like Hyp's Dad, he was hard on his son, likely causing his bullying behavior. It is also likely that, like his son, he is controlled by fear, which ended up influencing his son as well.
Mutt's father only makes one notable appearance, the rest being in various crowd shots throughout the movie. When the adults are defending the fleeing children during the Velociraptor attack, Mutt's father cowers in fear, allowing the raptors to pass by him and go after the kids and Hyp's father. Later, he continues to aid in the battle.