Manipulating and tailoring the intricate quasi-energy spectrum still remain a challenging issue in periodically-driven quantum systems. Here, we reported two typical spectral decompositions beyond the conventional adiabatic elimination, which enable to target the certain isolated quasi-energy bands by cutting-off the irrelevant far-off-resonant degrees of freedom. According to driving protocols in Floquet engineering, we classified the two non-adiabatic eliminations with Floquet driving frequency: namely, the quasi-adiabatic elimination, which non-adiabatically emerges at in-between driving frequency range, and in contrast the high-frequency-limited elimination, which requires rapidly-driven forces or modulations. Due to the failure of adiabatic condition, the protection mechanism of these driven eliminations is the first time to be demonstrated by selectively targeting the non-trivial isolated edge states via the bulk-edge correspondence, as a principle, from topological insulators and quantum field theories. Meanwhile, the near-field measurements using our well-fabricated photonic Floquet simulators correspondingly confirmed the observation of these eliminations and their stroboscopic dynamics. The non-adiabatic eliminations for Floquet quasi-energy spectrum are eventually proposed to open up the profound possibilities for artificially-controlling driven systems in topological Floquet engineering that may have numerous promising applications ranging from condensed matters to advanced photonics.