Game design speaking, Trynd's ulti renders him being immune to death itself when it is active via making his HP impossible to drop below a certain minimum threshold during the effect; on the other hand, Urgot's ulti just does a conditional check (measuring how much percentage of HP you have), and if passes it just does a ton of damage in a ramp fashion (upward to a maximum of I think 1,111,111). Hence since Trynd's HP can not drop below a certain point during ulti, it is not possible for Urgot's ulti to kill Trynd during the activation of the latter's ulti and he will tank the full damage. Similarly, Trynd can use ulti to escape many other situations that are typically certain death for others.
The only exception is the fountain laser, which it ignores all effects like damage immunity and whatnot, in order to prevent spawn camping/killing.
......
Lore speaking, Trynd is said to reach some kind of inhuman state when he's incredibly angry, maybe his body just becomes indestructible once he reaches that stage and meat grinders has no effect on him.