The energy conditions of mimetic-f(R) gravity theory, together with the Dolgov-Kawasaki instability will be analyzed. It will be shown that the condition for the stability of the theory against Dolgov-Kawasaki is equivalent to the standard f(R) gravity theory. We will also show that the exact de Sitter solution for the theory can only be obtained by an exponential form for the function f(R). The Brans-Dicke equivalence of the theory is also discussed in more details. We will obtain the parameter space of the theory in an exponential and power law forms of f(R), for violating the strong energy condition while satisfying the weak, null and dominant energy conditions.