Why does sour candy cut the roof of your mouth or cut the inside of your cheeks?

Because citric acid is some harsh stuff.

You can find it in shower cleaners.

While you might feel the effects of sour candy on your tongue, the stuff that makes you pucker is terrible for your teeth as well. Just like other candies, the amount of sugar is sour candy creates an environment that allows bad bacteria to increase in number, feeding off the sugar and eroding enamel.

Best guess on this will be the acid in the sweets.

There are sharp edges in hard candies. 

It doesn't.   Acid will break down your tissues,  but nothing is cut.  Simply put the same nerves are triggered with both cutting and breaking down. 

Hmm.. Because its jagged edges? Be careful not to hurt the gums and a food trap. Makes it harder to clean plus prettu sure could lead to a infection. 

Most likely due to an overload of citric acid.