The two-dimensional erosion of a vortex subjected to an external, adverse shear is studied experimentally. The flow takes place in a thin stratified layer; the vortex is produced by electromagnetic forcing, whereas the shear is driven mechanically. The system thus allows the vortex strength and the external shear to be controlled independently. We observe the so-called ‘erosion’ process, i.e. the progressive decrease of the vortex area, leaving the vortex core unaffected. This process is controlled by the ratio γ=S/ωmax, where ωmax and S are respectively the maximum vorticity of the vortex and the external shear. At small γ, the erosion is weak and the vortex survives over the duration of the experiment. At large γ, the vortex is first eroded, and then, after a critical time, becomes stretched and eventually breaks up into filaments. During the first period of time, the compensated maximum vorticity (with friction decay removed) is constant and the vortex area decreases, while beyond the critical time, both quantities decrease with time. A critical value for γ, defining the transition between these two regimes, is determined experimentally: γc=0.051±0.017. The breaking process itself, during which the vorticity of the vortex core decreases, is investigated. All the qualitative aspects of the erosion process, the onset of breaking and the breaking process itself are found to be in excellent agreement with the theoretical and numerical description. The experimental value of γc and the properties of the filamentation process are consistent with the numerical estimates.