Schizosaccharomyces pombe Casein kinase 1 (Hhp1) is a dual-specific kinase phosphorylating serine and threonine residues as well as tyrosine side chains. S. pombe Hhp1 kinase is homologous to Saccharomyces cerevisiae Hrr25, Drosophila double-time (dbt), and mammalian Casein kinase 1-epsilon (CKIε). CK1 enzymes regulate the circadian clock, Wnt (wingless) signalling, cell death, cell cycle progression and DNA repair. How one group of enzymes is able to execute so many functions is still poorly understood, especially because of the large number of isoforms and splice varinants in mammalian cells. This study uses the fission yeast as a model to research the roles of CK1 in the response to broken DNA replication forks. S.pombe Hhp1 is closely related to human CKIε and was previously implicated in DNA repair. A combination of genetic, biochemical and cell biological technologies revealed a novel role of Hhp1 kinase in the regulation of the DNA structure-specific endonuclease Mus81-Eme1. When DNA replication forks break in the presence of the topoisomerase 1 inhibitor camptothecin (CPT), Mus81-Eme1 acts on the broken chromosomes. Hhp1 is predicted to phosphorylate the regulatory subunit Eme1 jointly with the cell cycle regulator Cdc2 and the DNA damage checkpoint kinase Chk1. Genetic tests showed that all three kinases act in the same CPT-response pathway. The recreation of CK1 mutations of the circadian clock (hhp1.R180C, hhp1.P49S, and hhp1.M82I) and of CK1 mutations found in human breast cancers (hhp1.L51Q) in S.pombe Hhp1 revealed that different kinase activity levels are crucial for the regulation of DNA repair and cell cycle progression. While a limited drop in Hhp1 kinase activity, for example by widening its ATP binding site (methionine-84 to glycine), considerably delays the exit from a G2 arrest in the presence of damaged replication forks (CPT), it does not significantly impair DNA repair and cell survival. Only a dramatic drop in kinase activity, for example by replacing the active site residue lysine-40 with an arginine side chain, affects DNA repair and cell survival. How different kinase activity levels can have distinct biological outputs is discussed in the context of how CK1 recognises primed and acidic phosphorylation motifs. Taken together, the outcomes of this work imply that the complex phenotypes of CK1 mutations in the circadian clock or in cancer cells are caused by mutations which impact differently on its kinases activity.