How do I destroy a pirate haven?
Make sure your law is set to anti piracy, for Rome that's "Lex Claudia"
Move a land army to the location of the pirate haven.
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Set the army's stance to "Root out pirates" (it's the icon on the bottom right of the stances selection area). This will cost a base of 100 military power.
Your army will force the pirates to walk the plank and and the haven will be gone forever.