Quantum materials are characterized by intertwined orders, and a fundamental goal in condensed matter physics is to achieve their selective control in such a way that one order parameter can be tuned while leaving others largely unaffected. Although significant progress has been made in thermal equilibrium, realizing such control out of equilibrium remains highly challenging. Here we employed in situ tensile strain to selectively manipulate the photoinduced lattice dynamics associated with ferroelectric and magnetic orders in multiferroic BiFeO₃. By applying MeV ultrafast electron diffraction to freestanding BiFeO₃ membranes under tunable strain, we showed that tensile strain markedly suppresses the ultrafast photoinduced reduction of the ferroelectric displacement. By contrast, the photoinduced dynamics of the antiferrodistortive rotation of the oxygen octahedra, which modulates the magnetic order, remains insensitive to strain. Not only do these findings reveal distinct microscopic pathways underlying nonequilibrium multiferroic dynamics, they also establish tunable strain as an effective route for engineering ultrafast phase control in correlated materials.