Treating leftover fresh tuna like garbage, you nuts?
This. Do you keep the belly section? The ribs?
The triangular shaped section of meat that covers the guts is friggin delicious. Cut that and save it. Marinate in a little soyaki or something similar. Put it on the grill skin side down for a few minutes, flip and finish cooking it. It will take longer to cook because there's alot of fat in there. But the fat is the good part. It drips down, hits the flames and stirs up more fire. It will be the richest tuna you'll ever eat. I thank my Japanese uncle for turning me on to this delight.
After you've loined out the fish, go for the ribs. That rib section has meat all in between the axial bones. BBQ this and share with friends. Just put it on a plate with some forks as appetizer kind of food. They call it a Hawaiian Rib Roast. De li shus.
As for those pesky scraps...poke'. Look it up. It's very similar to ceviche.
Sorry for the diatribe but - waste not want not when it comes to the almighty tuna.