The micro-pipette aspiration technique is a classical experiment used to characterize the physical properties of inert fluids and biological soft materials such as cellular aggregates. The physical parameters of the fluid, as viscosity and interfacial tension, are obtained by studying how the fluid enters the pipette when the suction pressure is increased and how it relaxes when the suction pressure is put to zero. A mathematical model representative of the experiment is needed to extrapolate the physical parameters of the fluid-like matter; however, for biological materials as cells or cell aggregates mathematical models are always based on strong starting hypotheses that impact the significance of the identified parameters. In this article, starting from the bi-constituent nature of the cell aggregate, we derive a general mathematical model based of a Cahn–Hilliard–Navier–Stokes set of equations. The model is applied to describe quantitatively the aspiration-retraction dynamics of a cell-aggregate into and out of a pipette. We demonstrate the predictive capability of the model and highlight the impact of the assumptions made on the identified parameters by studying two cases: one with a non-wetting condition between the cells and the wall of the pipette (classical assumption in the literature) and the second one, which is more realistic, with a partial wetting condition (contact angle θs = 150°). Furthermore, our results provide a purely physical explanation to the asymmetry between the aspiration and retraction responses which is alternative to the proposed hypothesis of an mechano-responsive alteration of the surface tension of the cell aggregate.