We determined the electromechanical properties of a suspended graphene layer by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) measurements, as well as computational simulations of the graphene-membrane mechanics and morphology. A graphene membrane was continuously deformed by controlling the competing interactions with a STM probe tip and the electric field from a back-gate electrode. The probe tip-induced deformation created a localized strain field in the graphene lattice. STS measurements on the deformed suspended graphene display an electronic spectrum completely different from that of graphene supported by a substrate. The spectrum indicates the formation of a spatially confined quantum dot, in agreement with recent predictions of confinement by strain-induced pseudomagnetic fields.