These are VERY Glitchy, only take in open water away from rocks or map edge as you can easily lose your tame.
We lost two high lvl Mosa's with asc saddles because it picked them up (one at a time) and moved one beyond the map barrier and the other has disappeared into the ground somewhere. Definitely very buggy.
If we knew beforehand we'd have tried with turtles or at least kite to the open ocean.
It seems particularly bad when you aren't riding your Mosa (or Pleis I guess) and they get attacked by the squid. It seemed less glitchy when plain killing them, just don't dismount.
Use a Mosa to tame this beast. Let the Mosa get grabbed wait a couple seconds get off feed it black pearls. Have your mosa on follow lowest, swim a bit away from the Tuso after feeding it, when the Tuso lets go the Mosa will swim to you. Repeat until Tuso it tamed. Super easy!
You need two people, one for feeding the black pearls and the other to feed the turtle that is in the grasp of the Tusoteuthis, with sweet vegetable cake for the health and to feed it stimulates berries as well