Cell deformability is a label-free biomarker of cell state in physiological and disease contexts ranging from stem cell differentiation to cancer progression. Harnessing deformability as a phenotype for screening applications requires a method that can simultaneously measure the deformability of hundreds of cell samples and can interface with existing high throughput facilities. Here we present a scalable cell filtration device, which relies on the pressure-driven deformation of cells through a series of pillars that are separated by micron-scale gaps on the timescale of seconds: less deformable cells occlude the gaps more readily than more deformable cells, resulting in decreased filtrate volume which is measured using a plate reader. The key innovation in this method is that we design customized arrays of individual filtration devices in a standard 96-well format using soft lithography, which enables multiwell input samples and filtrate outputs to be processed with higher throughput using automated pipette arrays and plate readers. To validate high throughput filtration to detect changes in cell deformability, we show the differential filtration of human ovarian cancer cells that have acquired cisplatin-resistance, which is corroborated with cell stiffness measurements using quantitative deformability cytometry. We also demonstrate differences in the filtration of human cancer cell lines, including ovarian cancer cells that overexpress transcription factors (Snail, Slug), which are implicated in epithelial-to-mesenchymal transition; breast cancer cells (malignant versus benign); and prostate cancer cells (highly versus weekly metastatic). We additionally show how the filtration of ovarian cancer cells is affected by treatment with drugs known to perturb the cytoskeleton and the nucleus. Our results across multiple cancer cell types with both genetic and pharmacologic manipulations demonstrate the potential of this scalable filtration device to screen cells based on their deformability.