There’s an old wives’ tale that says you’ll get sick from refrozen meat. That’s wrong. That will only happen if you thaw the meat the wrong way such as leaving it out on a counter overnight, letting it sit at a temperature where bacteria will grow.
The actual truth is that it’s fine and part of normal procedures for many businesses. I often buy a whole turkey when they’re on sale for the holidays. It wouldn’t make any sense however for me to cook a whole one as it’s just me and my cat here. So I always thaw the turkey in the fridge, then cut it up and wrap portions, then refreeze them for later use.
Most every deep sea fish is processed similarly. Tunas for instance are caught in the ocean and flash frozen on factory ships. That way they don’t have to head for shore each day; they can continue to fish until they have a full load.
The fish are thawed, then cut. In Japan they use long tuna knives that resemble swords. Obviously this method couldn’t be done on a fish while it is frozen.
Now recall that you’ve probably seen frozen packages of tuna and other ocean fish in the supermarket. It should now be obvious that this fish has been frozen AT LEAST twice.