While magnetic skyrmions are often modeled as rigid particles, both experiments and micromagnetic simulations indicate their easy-to-deform characteristic, especially when their motion is restricted by defects. Here we establish a theoretical framework for the dynamics of magnetic skyrmions by incorporating the degrees of freedom related to deformation and predict well the current-driven dynamics of deformable skyrmions in the presence of line defects without any parameter fitting, where classical theories based on rigid-particle assumption deviate significantly. Further, we define an emergent property of magnetic skyrmions-flexibility and show that this property strongly modulates the depinning dynamics of skyrmions along a line defect with breaches. Our work explores the emergent mechanics of magnetic skyrmions and extends the current understanding on the dynamics of skyrmions interacted with defects.