Anti-CRISPR proteins (Acrs) inhibit CRISPR-Cas immune defenses, with almost all known Acrs acting on the Cas nuclease-CRISPR (cr)RNA ribonucleoprotein (RNP) complex. Here, we show that AcrVIB1 from Riemerella anatipestifer, the only known Acr against Cas13b, principally acts upstream of RNP complex formation by promoting unproductive crRNA binding followed by crRNA degradation. AcrVIB1 tightly binds to Cas13b but not to the Cas13b-crRNA complex, resulting in enhanced rather than blocked crRNA binding. However, the more tightly bound crRNA does not undergo processing and fails to activate collateral RNA cleavage even with target RNA. The bound crRNA is also accessible to RNases, leading to crRNA turnover in vivo even in the presence of Cas13b. Finally, cryoelectron microscopy (cryo-EM) structures reveal that AcrVIB1 binds a helical domain of Cas13b responsible for securing the crRNA, keeping the domain untethered. These findings reveal an Acr that converts an effector nuclease into a crRNA sink to suppress CRISPR-Cas defense.