Micropipette aspiration (MPA) is one of the gold standards for quantifying biological samples' mechanical properties, which are crucial from the cell membrane scale to the multicellular tissue. However, relying on the manipulation of individual home-made glass pipettes, MPA suffers from low throughput and no automation. Here, we introduce the sliding insert micropipette aspiration method, which permits parallelization and automation, thanks to the insertion of tubular pipettes, obtained by photolithography, within microfluidic channels. We show its application both at the lipid bilayer level, by probing vesicles to measure membrane bending and stretching moduli, and at the tissue level by quantifying the viscoelasticity of 3D cell aggregates. This approach opens the way to high-throughput, quantitative mechanical testing of many types of biological samples, from vesicles and individual cells to cell aggregates and explants, under dynamic physico-chemical stimuli.