The supersonic flow separating past a cylindrical afterbody generates a complex, compressible and highly turbulent flowfield. This flow models several realistic applications, such as the wake region behind projectiles, bullets and unpowered rockets. The flow is studied here via non-time-correlated instantaneous velocity vector fields obtained using stereo particle image velocimetry (SPIV). Two overlapping velocity vector fields are simultaneously acquired and stitched together to obtain a high-resolution velocity vector field of the full flow. Statistics derived from the measurements, including the mean velocities and turbulence statistics (such as the Reynolds stresses), are presented in order to study the overall flow organization and turbulence levels. The in-plane velocity component data are validated against planar PIV data obtained previously in the same facility. In order to gain further insight into the global organization of the flow, proper orthogonal decomposition (POD) is performed. The energy convergence and the structures found in the eigenmodes are used to gain insight into the organization of the flow that may not be apparent by observation of the mean flow statistics or the instantaneous images. The resulting eigenmodes of the POD analysis indicate that there is a dominant global axial pulsing motion.