We calculate the finite-temperature r-mode spectrum of a slowly rotating superfluid Newtonian neutron star neglecting the entrainment between neutron and proton liquid components (i.e., neglecting the off-diagonal element of the entrainment matrix). We show that for 'minimal' NS core composition (neutrons, protons, and electrons) only two m = 2 r-modes exist -normal mode, which is similar to ordinary r-mode in a nonsuperfluid star, and a superfluid temperature-dependent mode. Accounting for muons in the core dramatically modifies the oscillation spectrum, resulting in an infinite set of superfluid r-modes, whose frequencies vary with temperature. We demonstrate that the normal r-mode can exhibit avoided crossings with superfluid modes at certain 'resonance' temperatures, where it dissipates strongly, which leads to substantial suppression of the r-mode instability near these temperatures. The corresponding instability windows are calculated and discussed. 1 Following Gusakov et al. (2014a), by the normal r-modes of a superfluid NS we mean the modes which, at a given temperature, have properties similar to ordinary r-modes in the non-superfluid NSs. They correspond to co-motion of superfluid and normal liquid components, and their eigenfrequencies do not depend on temperature. Normal r-modes are most unstable. By superfluid inertial modes we understand inertial modes which show superfluid-like behaviour at a given temperature. The oscillations of such modes are mostly counter-moving, baryon current is almost zero, their eigenfrequencies depend on temperature. These modes have no analogue in nonsuperfluid NSs. Note that, with temperature variation, a given mode can switch from a 'superfluid' regime to 'normal' regime and vice versa, experiencing avoided-crossings with neighbouring modes.