Is there an order in which players have to mulligan based on who starts?

Yes, there is a specific order for mulligans based on turn order.

According to Core Rules Rule 118: "In turn order, players perform their Mulligan."

This means that the player designated to take the first turn performs their mulligan first. Once they have completed their process (setting aside cards, drawing replacements, and recycling the set-aside cards), the next player in turn order performs their mulligan, and so on until all players have finished.

Important Notes on the Process:

• Turn Order Establishment: As per Rule 116, turn order is determined before the mulligan phase begins.
• Recycling: When you perform your mulligan, you set aside up to two cards, draw new ones, and then recycle the cards you set aside. According to RiftJudge FAQ #3227, when you recycle cards during a mulligan, you shuffle only those recycled cards together and place them on the bottom of your deck; you do not shuffle your entire deck.
• Private Information: Per RiftJudge FAQ #2729, the cards you choose to mulligan are not public information; they are considered privately derived information.