We report on the observation of the spin-exchange dynamics of $^{171}mathrm{Yb}$ atoms in the ground state $^1mathrm{S}_0$ and in the metastable state $^3mathrm{P}_0$. We implement the mixed-dimensional two-orbital system using a near-resonant and magic-wavelength optical lattices, where the $^1mathrm{S}_0$ and $^3mathrm{P}_0$ atoms are itinerant in a one-dimensional tube and localized in three dimensions, respectively. By exploiting an optical Stern-Gerlach method, we observe the spin depolarization of the $^1mathrm{S}_0$ atoms induced by the spin-exchange interaction with the $^3mathrm{P}_0$ atom. Our work could open the way to the quantum simulation of the Kondo effect.