If multiple replacement and/or prevention effects could apply to a Dinosaur you control, you choose the order in which to apply those effects. For example, if another effect will prevent 1 damage that would be dealt to a Dinosaur, you may apply Temple Altisaur's effect to prevent all but 1 of that damage and then apply the other effect to prevent that 1 damage.

The effects of two Temple Altisaurs won't reduce the damage from one source below 1 damage.

Combat damage can be assigned to other Dinosaurs you control as normal, but most of that damage will be prevented. For example, if a 3/3 Dinosaur you control blocks a 5/5 creature with trample, the attacking player may assign 2 of that creature's combat damage to the player or planeswalker it's attacking and Temple Altisaur will prevent 2 of the 3 damage assigned to the defending Dinosaur.

If multiple sources would deal damage to another Dinosaur you control, all but 1 damage from each of those sources is prevented.