Lithospheric slab breakoff can occur in various styles including a horizontal ‘tearing’, where an initial weakness develops into tearing and laterally propagates along the slab. Slab tearing has been invoked to explain changes in plate kinematics in the Western Mediterranean and the tectonic uplift that led to the Messinian Salinity Crisis. However, this process remains debated regarding its surface signature and the physical parameters controlling its initiation and dynamics. Here, we use 3D thermo-mechanical modelling to investigate geodynamic parameters affecting the slab-tearing initiation and its lateral propagation, and to quantify the corresponding surface vertical motions. We find that an oblique convergence introduces an asymmetry that favors the initiation of one-sided slab tearing. The tectonic configuration of the overriding plate has little effect on the trench migration rate, and slab tearing can results purely from the negative buoyancy of the subducted slab. This force and the slab retreat it causes are enough to generate an arcuate plan-view shape to the orogen. The slab-tear propagation rate varies from 37-67 cm/yr. During propagation, the slab tearing depth increases along the subducting slab, with a shallow initial tear (80-150 km) and a deeper tear (170-200 km) on the opposite end. The time needed for the slab to detach completely is geologically fast (<2 Myr). The slab tearing can cause a prominent surface uplift of 0.5-1.5 km throughout the forearc region with an uplift rate of 0.23-2.16 mm/yr, which is consistent with the situation during the first stage of the Messinian Salinity Crisis.