If Haxorus uses its "Bring Down the Axe" attack while Temple of Sinnoh is in play and there is a Mist Energy attached to the Defending Pokemon, does it knock out the Defending Pokemon?
Yes. Even though Temple of Sinnoh turns off the text portion of Mist Energy, it still remains a Special Energy Card and meets the requirement for Bring Down the Axe.
Source: TPCi Rules Team (2024-09-12)

Relevant cards

Note: All applicable cards may not be listed below.
SV65_46
SV65_46
SWSH10_155
SWSH10_155
SV5_161
SV5_161