What kind of person denies food to the poor and needy?
It's not really a denial. It's not as if the people who want to get rid of the food stamp program are deliberately denying the poor access to food. If those who would otherwise receive food stamps were able to pay for said food, then they would be allowed to buy said food. So, though they cannot afford to buy food, they are not, legally or forcefully, being prevented from having access to or eating food.
Anyway, though I would have opposed the introduction of such a program (I would prefer to see some sort of updated workhouse for the long-term unemployed), I can't see the point of cutting it in one fell swoop. Better simply to gradually reduce the size and scope of the program. In addition, I would have it stipulate that only a 'survival diet' could be purchased through food stamps. Bread, water, a little cheap meat and a few greens.