We present a new study of the merger dynamics of Abell~1775 by analyzing the high-quality Chandra and XMM-Newton archival data. We confirm/identify an arc-shaped edge (i.e., the head) at $sim48$~kpc west of the X-ray peak, a split cold gas tail that extends eastward to $sim163$~kpc, and a plume of spiral-like X-ray excess (within about $81-324$~kpc northeast of the cluster core) that connects to the end of the tail. The head, across which the projected gas temperature rises outward from $3.39_{-0.18}^{+0.28}$~keV to $5.30_{-0.43}^{+0.54}$~keV, is found to be a cold front with a Mach number of $mathcal{M}sim0.79$. Along the surfaces of the cold front and tail, typical KHI features (noses and wings, etc.) are found and are used to constrain the upper limit of the magnetic field ($sim11.2~mu$G) and the viscosity suppression factor ($sim0.01$). Combining optical and radio evidence we propose a two-body merger (instead of systematic motion in a large-scale gas environment) scenario and have carried out idealized hydrodynamic simulations to verify it. We find that the observed X-ray emission and temperature distributions can be best reproduced with a merger mass ratio of 5 after the first pericentric passage. The NAT radio galaxy is thus more likely to be a single galaxy falling into the cluster center at a relative velocity of 2800~$rm km~s^{-1}$, a speed constrained by its radio morphology. The infalling subcluster is expected to have a relatively low gas content, because only a gas-poor subcluster can cause central-only disturbances as observed in such an off-axis merger.
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