Recently, "squeezing" the light into deeply subwavelength volumes through excitation of plasmon-polaritons has been intensively studied due to a high potential for applications requiring a strong light-matter interaction . Although modern fabrication and excitation techniques allow for the light confinement into atomically-thin layers of 2D materials, the advantages of such nano-gap confinement are still largely unexplored from the practical perspective. In this paper, we propose an ultra-compact plasmonic switch, based on the non-trivial interference between the gap plasmons and graphene plasmons in the nanocavity, and having a footprint thousand times smaller than the free space wavelength. Full wave finite element method-based electromagnetic simulation was performed to study transmission properties of the device and reveal the underlying operation mechanism. As shown in the schematic, the graphene plasmon cavity is sandwiched by two metal-insulator-metal waveguide structures with nano-gap separation. The thickness of the insulator and metal layers are sufficiently small to support only fundamental transverse magnetic mode and observe transmission dip at a range of low Fermi level. The input signal is the plasmonic waveguide mode with a wavelength of 7.5 um. As shown in the transmission spectrum, total transmittance is tunable through electrostatically controllable Fermi level modulation. Fermi level affects two cavity modes, one is conventional Fabry-Perot transmission of graphene plasmon and the other is gap plasmon cavity mode emerged by strong nano-gap confinement. Unlike graphene plasmon Fabry-Perot transmission, modulation of nano-gap cavity mode is achievable through enhanced light-matter interaction by strong confinement. Since those modes have different amplitude modulation behavior and opposite sign at phase, it is possible to obtain huge transmission modulation, via controlling the weight of each strength of modes. In this paper, we show that competition between graphene plasmon cavity mode and nano-gap induced highly confined gap plasmon cavity mode provides excellent modulation performance even < 10 nm of gap size. We hope that emerged cavity induced by nano-gap interaction will change the conventional design scheme and expand a variety of design strategies.