Fast sawtooth crash of m = 1 mode (tens of µs) is a common MHD phenomenon in the core of tokamak plasma. In KSTAR plasmas with localized heating and current drive close to the sawtooth inversion radius (ρinv), very slow sawtooth crashes are observed with time scales of a few ms. Scan of heating deposition along with power modulation revealed two different mechanisms of the slow crash with the help of detailed 2D imaging diagnostics. The slow crash appears with slow heat transport of the remained m = 1 mode after the partial crash of outer multiple m/n = 1 modes, or with the growth of an island formed on ρinv when the heating deposition locates just inside ρinv or just outside ρinv. In the heating power modulation experiment, the slow crash with the island was sustained for the redistribution time scale of the driven current by a very short blip of heating.