A hallmark of type I CRISPR–Cas systems is the presence of Cas3, which contains both the nuclease and helicase activities required for DNA cleavage during interference. In subtype I-D systems, however, the histidine-aspartate (HD) nuclease domain is encoded as part of a Cas10-like large effector complex subunit and the helicase activity in a separate Cas3’ subunit, but the functional and mechanistic consequences of this organisation are not currently understood. Here we show that the Sulfolobus islandicus type I-D Cas10d large subunit exhibits an unusual domain architecture consisting of a Cas3-like HD nuclease domain fused to a degenerate polymerase fold and a C-terminal domain structurally similar to Cas11. Crystal structures of Cas10d both in isolation and bound to S. islandicus rod-shaped virus 3 AcrID1 reveal that the anti-CRISPR protein sequesters the large subunit in a non-functional state unable to form a cleavage-competent effector complex. The architecture of Cas10d suggests that the type I-D effector complex is similar to those found in type III CRISPR–Cas systems and that this feature is specifically exploited by phages for anti-CRISPR defence.