We study the escape problem of a bistable sawtooth system driven by correlated multiplicative and additive white noises. Exact analytic representation of the relative escape rate is obtained. Some novel phenomena are found from the calculation result; “suppression platform” appears in the relative escape rate when the noise correlation coefficient λ is positive. Moreover, for small positive values of λ, the relative escape rate exhibits “suppression platform” and then “resonant activation” with the increasing noise strength ratio R.