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Ukrainians aim to retake Crimea . Blowing up the bridge between Russia and Crimea have caused a collapse of Russian Logistic . They can't supply the troops in Crimea and southern front ( due to rail there being in range of Ukraine weapons ) to be in any figthing shape . 
They even made sure the bridge is just partially damaged to allow Russian forces and sympathizers to have a retreat option like in other operations .
What kind of armaments do you imagine Ukraine having that could make a harbour unusable? 
They might be able to take out a few warehouses, maybe a bit of rail or if they hit the harbour with everything they have a pier.
You need some serious tonnage to make a harbour unusable. Like nuke scale tonnage and even that would probably only make the harbour unusable due to radiation. It's like trying to sink a piece of land. >

Send in divers and plant mines? >

Damage a ship, or maybe two? Before the harbour is cleared by Russian divers. Not at all a bad idea if the Ukrainians have the means. But it will in no way make the harbour unusable. >

It would not endear the residents of Crimea to Ukraine if it ever regained the territory. And I don’t think Ukraine’s military situation is at all desperate enough for such a move.