Disease can induce changes to subcellular components, altering cell phenotype and leading to measurable bulk-material mechanical properties. The mechanical phenotyping of single cells therefore offers many potential diagnostic applications. Cells are viscoelastic and their response to an applied stress is highly dependent on the magnitude and timescale of the actuation. Microfluidics can be used to measure cell deformability over a wide range of flow conditions, operating two distinct flow regimes (shear and inertial) which can expose subtle mechanical properties arising from subcellular components. Here, we investigate the deformability of three colorectal cancer (CRC) cell lines using a range of flow conditions. These cell lines offer a model for CRC metastatic progression; SW480 derived from primary adenocarcinoma, HT29 from a more advanced primary tumor and SW620 from lymph-node metastasis. HL60 (leukemia cells) were also studied as a model circulatory cell, offering a non-epithelial comparison. We demonstrate that microfluidic induced flow deformation can be used to robustly detect mechanical changes associated with CRC progression. We also show that single-cell multivariate analysis, utilising deformation and relaxation dynamics, offers potential to distinguish these different cell types. These results point to the benefit of multiparameter determination for improving detection and accuracy of disease stage diagnosis.