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Abstract: Coherent magnon-photon coupling under the Floquet drive has been demonstrated in recent experimental measurements and theoretical calculations. In this work, we studied the Floquet-driven dissipative cavity magnonics theoretically. Our results show that the Floquet states ${d}^{(n)}$ ($n$ is integer) with dissipative coupling give rise to many level attractions in the transmission spectrum. As driving amplitude increases or driving frequency decreases, the coupling for the $n=0$ mode becomes weak while for the sideband $(n=\ifmmode\pm\else\textpm\fi{}1)$ becomes strong due to renormalized coupling strength. When the coherent and the dissipative couplings are simultaneously present, a series of sharp dips originating from the interference of two couplings occur, in contrast to a single dip with zero damping in previous work. The modified zero-damping condition is derived for the Floquet system. Moreover, we give a generalized selection rule for coupling between Floquet states by considering the multiphoton process that has not yet been studied in previous work. Our results open up promising roads for exploring the dissipative magnon-photon coupling with the Floquet driving technology.