Csm, a type III-A CRISPR-Cas interference complex, is a CRISPR RNA (crRNA)-guided RNase that also possesses target RNA-dependent DNase and cyclic oligoadenylate (cOA) synthetase activities. However, the structural features allowing target RNA-binding-dependent activation of DNA cleavage and cOA generation remain unknown. Here, we report the structure of Csm in complex with crRNA together with structures of cognate or non-cognate target RNA bound Csm complexes. We show that depending on complementarity with the 5' tag of crRNA, the 3' anti-tag region of target RNA binds at two distinct sites of the Csm complex. Importantly, the interaction between the non-complementary anti-tag region of cognate target RNA and Csm1 induces a conformational change at the Csm1 subunit that allosterically activates DNA cleavage and cOA generation. Together, our structural studies provide crucial insights into the mechanistic processes required for crRNA-meditated sequence-specific RNA cleavage, RNA target-dependent non-specific DNA cleavage, and cOA generation.