First of all the Wiener filter does not remove the noise but (hopefully) reduce it.

It does this based on the relationship between the power spectral density of the clean signal $x[n]$ and imposed noise $v[n]$. The frequency response of a noncausal IIR Wiener filter is given as

$$ H(\omega) = \frac{ P_x(\omega) }{ P_x(\omega) + P_v(\omega) } $$

where $P_x$ and $P_v$ are PSDs of clean signal and uncorelated noise imposed on it. As can be seen, the filter spectrum involves all the bands including where noise and signal spectrums are overlapping too, and that's one of the benefits of using such an advanced tool.

First of all the Wiener filter does not remove the noise but reduce it for WSS signals.

It does this based on the relationship between the power spectral density of the clean signal $x[n]$ and imposed noise $v[n]$, both assumed as WSS. The frequency response of a noncausal IIR Wiener filter is given as

$$ H(\omega) = \frac{ P_x(\omega) }{ P_x(\omega) + P_v(\omega) } $$

where $P_x$ and $P_v$ are PSDs of clean signal and uncorelated noise imposed on it. As can be seen, the filter spectrum involves all the bands including where noise and signal spectrums are overlapping too, and that's one of the benefits of using such an advanced tool.

Note that this is not a non-destructive noise reduction and it wont necessarily preserve the waveform of the clean signal, but its PSD is improved; made closer to clean signal's PSD.