Once you begin to cast a spell, losing control of Muldrotha won't affect the spell.

Use the type of the card as it's played or cast to determine which permanent type to count it as. For example, if you cast a creature spell from your graveyard, you can cast a card with bestow as an enchantment spell.

For example, you may cast an artifact creature spell as your artifact spell and cast another artifact creature spell as your creature spell.

If a permanent card is put into your graveyard during your main phase and the stack is empty, you have a chance to cast it before any player may attempt to remove that card from your graveyard.

If multiple effects allow you to play a card from your graveyard, you must announce which permission you're using as you begin to play the card.

You must follow the normal timing permissions and restrictions of the cards you play from your graveyard. For example, you can't use Muldrotha to play a land if you don't have an available land play or to cast a planeswalker spell during your end step.

If you play a card from your graveyard and then have a new Muldrotha come under your control in the same turn, you may play another land or spell of that type from your graveyard that turn.

You must pay the costs to cast a spell this way. If it has an alternative cost, you may cast it for that cost instead.