Battlegate Mimic

• WWizards of the Coast2008-08-01
  Official Ruling
  The ability triggers whenever you cast a spell that’s both of its listed colors. It doesn’t matter whether that spell also happens to be any other colors.
• WWizards of the Coast2008-08-01
  Official Ruling
  If you cast a spell that’s the two appropriate colors for the second time in a turn, the ability triggers again. The Mimic will once again become the power and toughness stated in its ability, which could overwrite power- and toughness-setting effects that have been applied to it in the meantime.
• WWizards of the Coast2008-08-01
  Official Ruling
  Any other abilities the Mimic may have gained are not affected.
• WWizards of the Coast2009-10-01
  Official Ruling
  The effect from the ability overwrites other effects that set power and/or toughness if and only if those effects existed before the ability resolved. It will not overwrite effects that modify power or toughness (whether from a static ability, counters, or a resolved spell or ability), nor will it overwrite effects that set power and toughness which come into existence after the ability resolves. Effects that switch the creature’s power and toughness are always applied after any other power or toughness changing effects, including this one, regardless of the order in which they are created.

Rulings via Scryfall