SO, I read through this thread and was wondering if any one has proven that mermaids do indeed breed. if they do it seems quite straightforward on how to catch them, as well as butcher them.
Build a straight shoreline where they seem most likely to be washed ashore, build a single row of pumps to get this shoreline emty. place traps beneath the shore, aswell as above it to be sure to catch any that enter. refill with water.
This should then allow you to catch them either into the submerged cages, or the shore-sided ones.
cages are then brought to the cage area and the mermaids chained into a 3/7 waterfilled room til the more permanent solution is done. Since they cannot be tamed (if they can that is awesome), there is a simple solution of how to separate the young from their mothers.
Imagine a 3x3x2 room. iIn the middle is a pillar with the chained mermaid. Around the pillar there are hatches connected to a lever. The room is filled with water. Once the lever is pulled the hatches open and the water aswell as the youngling is dropped to the room below. the lever is then pulled again and the chamber refilled. to avoid drowning you just make sure that there is a constant waterfall on the spot with the chained mermaid constantly, and thus a simple drain on the floor below to ensure that water is not flooding your fort. ideally a system that keeps the water at 3-4/7 at all times. this lower room is of course unescapable for you mermaid children, since they cannot leave the water. So there is no need to hurry, your hunters will get to them eventually...
This has the benefit of allowing your dwarves the spectacular experience of indoor mermaid hunting, where ridiculously valued game is hunted within an enclosed area for the benefit of the rich.
It also allows you to use the meat, skin and fat, and not only the bones.
and even better is that you could seal of the room to stop your hunters, and instead open a door leading to the sea to allow your youngsters to be led into a cage trap and brought to a separate room for later grooming.