Close encounters between stellar-mass black holes (BHs) and stars occur frequently in dense star clusters and in the disks of active galactic nuclei. Recent studies have shown that in highly eccentric close encounters, the star can be tidally disrupted by the BH in a microtidal disruption event (microTDE), resulting in rapid mass accretion and possibly bright electromagnetic signatures. Here we consider a scenario in which the star might approach the stellar-mass BH in a gradual, nearly circular inspiral, under the influence of dynamical friction in a circum-binary gas disk or three-body interactions in a star cluster. We perform hydrodynamics simulations of this scenario using the smoothed particle hydrodynamics code PHANTOM. We find that under certain circumstances (for initial eccentricity e 0 ≳ 0.4 and penetration factor β = 1, or e 0 < 0.4 and β ≲ 0.67), the mass of the star is slowly stripped away by the BH. We call this gradual tidal disruption a “tidal-peeling event.” Additionally, we discover that some low-eccentricity microTDEs (e 0 < 0.4 and β = 1) are a new form of fast luminous transients similar to parabolic microTDEs. Depending on the initial distance and eccentricity of the encounter, these low-eccentricity microTDEs might exhibit significant accretion rates and orbital evolution distinct from those of a typical (eccentric) microTDE.