Spike trains of retinal ganglion cells (RGCs) are the sole source of visual information to the brain; and understanding how the ∼20 RGC types in mammalian retinae respond to diverse visual features and events is fundamental to understanding vision. Suppressed-by-contrast (SbC) RGCs stand apart from all other RGC types in that they reduce rather than increase firing rates in response to light increments (ON) and decrements (OFF). Here, we genetically identify and morphologically characterize SbC-RGCs in mice, and target them for patch-clamp recordings under two-photon guidance. We find that strong ON inhibition (glycine > GABA) outweighs weak ON excitation, and that inhibition (glycine > GABA) coincides with decreases in excitation at light OFF. These input patterns explain the suppressive spike responses of SbC-RGCs, which are observed in dim and bright light conditions. Inhibition to SbC-RGC is driven by rectified receptive field subunits, leading us to hypothesize that SbC-RGCs could signal pattern-independent changes in the retinal image. Indeed, we find that shifts of random textures matching saccade-like eye movements in mice elicit robust inhibitory inputs and suppress spiking of SbC-RGCs over a wide range of texture contrasts and spatial frequencies. Similarly, stimuli based on kinematic analyses of mouse blinking consistently suppress SbC-RGC spiking. Receiver operating characteristics show that SbC-RGCs are reliable indicators of self-generated visual stimuli that may contribute to central processing of blinks and saccades. Significance Statement: This study genetically identifies and morphologically characterizes suppressed-by-contrast retinal ganglion cells (SbC-RGCs) in mice. Targeted patch-clamp recordings from SbC-RGCs under two-photon guidance elucidate the synaptic mechanisms mediating spike suppression to contrast steps, and reveal that SbC-RGCs respond reliably to stimuli mimicking saccade-like eye movements and blinks. The similarity of responses to saccade-like eye movements and blinks suggests that SbC-RGCs may provide a unified signal for self-generated visual stimuli.