The series of molecular signals induced by granzymes which triggers the cell death of a cell. The pathway starts with reception of a granzyme signal, and ends when the execution phase of cell death is triggered. Granzymes are serine proteases that are secreted by cytotoxic T cells and natural killer cells to induce cell death in target cells. [ http://www.ncbi.nlm.nih.gov/pubmed/32299851 ]