Does mana stay in your mana pool after the land has been destroyed
Yes, it will stay in your mana pool until the end of the current step or phase.

There are effects that empty your mana pool, but they specifically say so, such as Mana Short.


  106.4. When an effect produces mana, that mana goes into a player’s mana pool. From there, it can be used to pay costs immediately, or it can stay in the player’s mana pool. Each player’s mana pool empties at the end of each step and phase.