Microtubules have spatiotemporally complex posttranslational modification patterns. How cells interpret this tubulin modification code is largely unknown. We show that C. elegans katanin, a microtubule severing AAA ATPase mutated in microcephaly and critical for cell division, axonal elongation, and cilia biogenesis, responds precisely, differentially, and combinatorially to three chemically distinct tubulin modifications-glycylation, glutamylation, and tyrosination-but is insensitive to acetylation. Glutamylation and glycylation are antagonistic rheostats with glycylation protecting microtubules from severing. Katanin exhibits graded and divergent responses to glutamylation on the α- and β-tubulin tails, and these act combinatorially. The katanin hexamer central pore constrains the polyglutamate chain patterns on β-tails recognized productively. Elements distal to the katanin AAA core sense α-tubulin tyrosination, and detyrosination downregulates severing. The multivalent microtubule recognition that enables katanin to read multiple tubulin modification inputs explains in vivo observations and illustrates how effectors can integrate tubulin code signals to produce diverse functional outcomes.