One missile hit equipped with what is probably a smallish conventional warhead, is not gong to sink a 100,000 ton warship. Will it cause millions of dollars of damage? Yes it will. Will it cause the ship to be nonoperational? Yes for a while.
You would have to shoot it like an unguided torpedo. You could make fractional adjustments but even with a computer, Mach 7 is too fast for terminal adjustments.
You blow up an AA warhead in front of it and it is running into a cloud of shrapnel at about Mach 10. It will be ripped to shreds. The concussion could also send it out of control.