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We formulate a supersymmetric version of gravity with mimetic dark matter. The coupling of a constrained chiral multiplet to N = 1 supergravity is made locally supersymmetric using the rules of tensor calculus. The chiral multiplet is constrained with a Lagrange multiplier multiplet that could be either a chiral multiplet or a linear multiplet. We obtain the fully supersymmetric Lagrangians in both cases. It is then shown that the system consisting of the supergravity multiplet, the chiral multiplet and the Lagrange multiplier multiplet can break supersymmetry spontaneously leading to a model of a graviton, massive gravitino and two scalar fields representing mimetic dark matter. The combination of the chiral multiplet and Lagrange multiplier multiplet can act as the hidden sector breaking local N = 1 supersymmetry. [ABSTRACT FROM AUTHOR]