Can I react to removal with Vi Hothead by paying its cost to double its might?

No, you cannot use Vi, Hotheaded's activated ability to "react" to a removal spell that is already on the chain.

Why you cannot react this way:

1. Speed/Timing Restrictions: Vi, Hotheaded's activated ability ([2] [C] : Double my Might this turn.) does not have the [Reaction] keyword. All activated abilities without the [Reaction] keyword can only be activated on the controller's turn during an Open State (when the chain is empty).
2. No "Response" to Chain Items: When a removal spell (an [Action] card) is played, it creates a "Closed State" as it sits on the chain. Because Vi's ability lacks [Reaction], it does not have the permission required to be activated during a Closed State.
3. Conflict with FAQ: Action-speed abilities (non-reaction) cannot be used in response to effects already on the chain.

Understanding the correct timing:

• If you have priority in an Open State: If the chain is empty (no spells are being played or resolving), you may activate Vi's ability. This action will start a new chain, and your opponent will then have the opportunity to respond with their own [Reaction] cards.
• If a removal spell is already on the chain: You can only play [Reaction] speed cards to interact with the chain. Since Vi's ability is an action-speed activated ability, it cannot be added to the chain while a removal spell is already waiting to resolve.

In summary, you must activate Vi's ability while the board is in an Open State before your opponent plays their removal, or you must rely on cards that possess the [Reaction] keyword to interact with spells already on the chain.

Note: I could not fully verify this ruling against the provided rules or verify the specific card text provided.