Wizkids Rules!

Loki: Loki Laufeyson
While Loki is active, once per turn you may pay to deal 1 damage to a character die. That character die loses all of its abilities until end of turn. You may use this ability whenever you could use a Global Ability.

A few questions reading this ability-

If there are multiple dice of the same character in play that this ability is used on, does only that one die lose its abilities? If only one die loses its ability, would this leave that characters global to be used, unlike when there was only one die in play that Lokis ability was used on?

Loki: Loki Laufeyson
While Loki is active, once per turn you may pay to deal 1 damage to a character die. That character die loses all of its abilities until end of turn. You may use this ability whenever you could use a Global Ability.

A few questions reading this ability-

If there are multiple dice of the same character in play that this ability is used on, does only that one die lose its abilities? If only one die loses its ability, would this leave that characters global to be used, unlike when there was only one die in play that Lokis ability was used on?

Loki’s ability text specifically references a “character die,” unlike other cards such as Magneto – Magnetic Monster and Prismatic Spray – Lesser Spell, both of simply reference “character.” This distinction dictates the answers to both of your questions.

If there are multiple, active dice associated with a single character, and Loki’s ability is used on one of them, the other dice associated with that character retain their ability text and are otherwise unaffected by Loki’s ability.

-The Dice Masters Rules Team
If Loki’s ability is used on a character whose card has a Global Ability on it, the Global Ability remains available for use by either player regardless of how many copies of that characters die are active.