It's falling apart because the fat layers aren't elastic enough to hold the muscle layers together at the tolerance you cut it.

That means you have to either cut it thicker(which assumes the salmon was firm before you cut it), eat it sooner(so the fat will no break down), keep it colder(might have been a problem if the fish was room temp), or use a different variety of salmon.

We had salmon that would do that at the sushi bar. We called it "Spicy Salmon Roll".