자르다 : to divide something into two pieces with a sharp-edged instrument 썰다 : to slice, to make something into smaller slices with knife or saw (usually repeated action) 머리카락을 자르다(O) 머리카락을 썰다(X)

When we cut sth, mostly kind of food ingredients, with a nife, we use "썰다." ex. 나는 된장찌개에 넣을 파를 썰고 있다. When we cut sth with scissors, we use "자르다.” ex. 머리를 자르다 / 종이를 자르다