We study a Jackiw-Teitelboim (JT) supergravity theory, defined as a Euclidean path integral over orientable supermanifolds with constant negative curvature, which was argued by Stanford and Witten to be captured by a random matrix model in the β=2 Dyson-Wigner class. We show that the theory is a double-cut matrix model tuned to a critical point where the two cuts coalesce. Our formulation is fully nonperturbative and manifestly stable, providing for explicit unambiguous computation of observables beyond the perturbative recursion relations derivable from loop equations. Our construction shows that this JT supergravity theory may be regarded as a particular combination of certain type 0B minimal string theories, and is hence a natural counterpart to another family of JT supergravity theories recently shown to be built from type 0A minimal strings. We conjecture that certain other JT supergravities can be similarly defined in terms of double-cut matrix models.