Immune systems must recognize and destroy different pathogens that threaten the host. CRISPR-Cas immune systems protect prokaryotes from viral and plasmid infection utilizing small CRISPR RNAs that are complementary to the invader’s genome and specify the targets of RNA-guided Cas nucleases. Type III CRISPR-Cas immunity requires target transcription, and whereas genetic studies demonstrated DNA targeting, in vitro data have shown crRNA-guided RNA cleavage. The molecular mechanism behind these disparate activities is not known. Here, we show that transcription across the targets of the Staphylococcus epidermidis type III-A CRISPR-Cas system results in the cleavage of the target DNA and its transcripts, mediated by independent active sites within the Cas10-Csm ribonucleoprotein effector complex. Immunity against plasmids and DNA viruses requires DNA, but not RNA, cleavage activity. Our studies reveal a highly versatile mechanism of CRISPR immunity that can defend microorganisms against diverse DNA and RNA invaders. Display omitted •Type III CRISPR-Cas systems provide immunity when the target DNA is transcribed•The type III Cas10-Csm complex performs co-transcriptional RNA-guided DNA cleavage•The complex is also capable of RNA-guided RNA cleavage•Both the target DNA and its transcript are subject to RNA-guided cleavage in vivo The type III-A CRISPR-Cas system is capable of RNA-guided DNA and RNA cleavage in vivo, revealing a highly versatile mechanism of CRISPR immunity that protects microorganisms against diverse DNA and RNA invaders.