Significant transition strength in light α-conjugate nuclei at low energy, typically below 10 MeV, has been observed in many experiments. In this work the isoscalar low-energy response of N=Z nuclei is explored using the finite amplitude method based on the microscopic framework of nuclear energy density functionals. Depending on the multipolarity of the excitation and the equilibrium deformation of a particular isotope, the low-energy strength functions display prominent peaks that can be attributed to cluster mode structures: α+C12+α and α+O16 in Ne20, C12+C12 in Mg24, 4α+C12 in Si28, etc. Such cluster modes are favored in light nuclei with large deformation.