We study how environment regulates the star formation cycle of 33 Virgo Cluster satellite galaxies on 720 pc scales. We present the resolved star-forming main sequence for cluster galaxies, dividing the sample based on their global H i properties and comparing to a control sample of field galaxies. H i-poor cluster galaxies have reduced star formation rate (SFR) surface densities with respect to both H i-normal cluster and field galaxies (∼0.5 dex), suggesting that mechanisms regulating the global H i content are responsible for quenching local star formation. We demonstrate that the observed quenching in H i-poor galaxies is caused by environmental processes such as ram pressure stripping (RPS), simultaneously reducing the molecular gas surface density and star formation efficiency (SFE) compared to regions in H i-normal systems (by 0.38 and 0.22 dex, respectively). We observe systematically elevated SFRs that are driven by increased molecular gas surface densities at fixed stellar mass surface density in the outskirts of early stage RPS galaxies, while SFE remains unchanged with respect to the field sample. We quantify how RPS and starvation affect the star formation cycle of inner and outer galaxy disks as they are processed by the cluster. We show both are effective quenching mechanisms, with the key difference being that RPS acts upon the galaxy outskirts while starvation regulates the star formation cycle throughout disk, including within the truncation radius. For both processes, the quenching is caused by a simultaneous reduction in the molecular gas surface densities and SFE at fixed stellar mass surface density.