If a very distant supernova has a high Doppler effect redshift do our eyes see its evolution picture like in 'slow motion'?

The wavelengths of the light from the supernova are redshifted by a factor of $1+z$. The duration of the supernova is also increased by the same factor of $1+z$.

The problems with establishing this relationship are that all supernovae (even type Ia) are not identical and their light curve shapes/durations depend on intrinsic wavelength.

However, the available data appear to support this relationship (e.g. Blondin et al. (2008). A plot from this paper is what you are looking for. It shows a parameter expressing how quickly a type Ia supernova light curve evolves versus $(1+z)^{-1}$.