I was taught to hold with the blade in the same direction as the cut, or the stab and rip eg, a yokoman attack, although starting with a stab in ... to get the thing IN ... is followed by the diagonal cut down and across the body. A thrust in, at a lower target and you cut up, visa versa.
I think the idea is that when someone knows how to use a knife they arent just going to cut you or poke you ... they are REALLY going to do some serious damage, hence the grip, blade orientation and follow through.
I know some systems slice on the surface, but they usually do something like this for example - slice, down on the attacking wrist, blocking or deflecting the attack, slice up further up the arm, slice down further up the arm, slice up the undershoulder muscle, slice down the throat ...... all in about .5 of a second.
But Aikido mostly seems to attack with the knife in the traditional Japanese way ???