Cellular mechanical properties (e.g. compressibility) are important biophysical markers in relation to cellular processes and functionality. Among the methods for cell mechanical measurement, acoustofluidic methods appear to be advantageous due to tunability, biocompatibility and acousto-mechanical nature. However, the previous acoustofluidic methods were limited in throughput and number of measurements. In this study, we developed a high-throughput microfluidic compressibility cytometry approach using multi-tilted-angle surface acoustic wave, which can provide thousands of single-cell compressibility measurements within minutes. The compressibility cytometer was constructed to drag microparticles or cells towards the microfluidic channel sidewall at different segments based on their biophysical properties (such as size and compressibility), as a result of the varied balance between acoustics and flow. Mathematical analysis and computational simulation revealed that the compressibility of a cell could be estimated from the position of collision with the sidewall. Microbeads of different materials and sizes were experimentally tested to validate the simulation and to demonstrate the capability to characterise size and compressibility. MDA MB231 cells, of the triple negative breast cancer subtype, were treated with the microtubule disrupting agent colchicine which increased compressibility and treated with the actin disrupting agent cytochalasin B which increased cell size but did not change compressibility. Moreover, the highly metastatic variant MDA MB231 LNm5 cell line showed increased compressibility compared to the parent MDA MB231 cells, indicating the potential utility of high-throughput mechanophenotyping for tumour cell characterisation.