Forkhead-associated (FHA) domains recognize phosphothreonines, and SQ/TQ cluster domains (SCDs) contain concentrated phosphorylation sites for ATM/ATR-like DNA-damage-response kinases. The Rad53-SCD1 has dual functions in regulating the activation of the Rad53-Dun1 checkpoint kinase cascade but with unknown molecular mechanisms. Here we present structural, biochemical, and genetic evidence that Dun1-FHA possesses an unprecedented diphosphothreonine-binding specificity. The Dun1-FHA has >100-fold increased affinity for diphosphorylated relative to monophosphorylated Rad53-SCD1 due to the presence of two separate phosphothreonine-binding pockets. In vivo, any single threonine of Rad53-SCD1 is sufficient for Rad53 activation and RAD53-dependent survival of DNA damage, but two adjacent phosphothreonines in the Rad53-SCD1 and two phosphothreonine-binding sites in the Dun1-FHA are necessary for Dun1 activation and DUN1-dependent transcriptional responses to DNA damage. The results uncover a phospho-counting mechanism that regulates the specificity of SCD, and provide mechanistic insight into a role of multisite phosphorylation in DNA-damage signaling.