Here, there will be two replacement effects that replace Uril being destroyed with something else, and both are totem armor effects from Hyena Umbra and Spider Umbra (C.R. 616.1, 702.88a). If you control Uril, you choose which effect applies (and thus which Aura is destroyed), either Hyena Umbra's or Spider Umbra's (C.R. 616.1d, 616.1), and the other effect won't apply anymore since Uril won't be destroyed anymore (C.R. 616.1e). (Note that totem armor is not the same as regeneration, even though both effects replace being destroyed with something else [compare C.R. 702.88a with C.R. 701.13, respectively], so Wrath of God's effect that provides that creatures destroyed by it "can't be regenerated" doesn't apply to totem armor.)
So you are saying that if I have multiple instances of Totem Armor I would only lose one enchantment than gives it?
Yes. In your scenario, if Uril would be destroyed, instead you remove its damage and choose one of the two Auras to destroy -- you can't choose to destroy none or both (totem armor is not optional [review C.R. 702.88a]).
EDIT (Apr. 8): Clarification.