Second-order topological semimetals (SOTSMs) is featured with the presence of hinge Fermi arc. How to generate SOTSMs in different systems has attracted much attention. We here propose a scheme to create exotic SOTSMs by periodic driving. It is found that novel Dirac SOTSMs with a widely tunable number of nodes and hinge Fermi arcs, the adjacent nodes with same chirality, and the coexisting nodal points and nodal loops can be generated at ease by the periodic driving. When the time-reversal symmetry is broken, our scheme also permits us to realize an exotic hybrid-order Weyl semimetals with the coexisting hinge and surface Fermi arcs. The multiplicity of the zero- and $pi/T$-mode Weyl points endows our system more colorful 2D sliced topological phases, which can be any combination of normal insulator, Chern insulator, and SOTI, than the static case. Enriching the family of topological semimetals, our scheme supplies a convenient way to artificially synthesize and control exotic topological phases by periodic driving.
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