  Within the multiple scattering formulation, the incoherent pion production in
neutrino-deuteron reactions at energies near the $\Delta(1232)$ resonance is
investigated. The calculations include an impulse term and one-loop
contributions from nucleon-nucleon ($NN$) and pion-nucleon ($\pi N$) final
state interactions. The input amplitudes of $\pi N$ scattering and electroweak
pion production reaction on nucleon are generated from a dynamical model which
describes very extensive data of $\pi N$ scattering and both the
electromagnetic and the weak pion production reactions on the nucleon. The $NN$
scattering amplitudes are generated from the Bonn potential. The validity of
the calculational procedures is established by giving a reasonably good
description of the data of pion photo-production on the deuteron. The
constructed model is then applied to predict the cross sections of $\nu + d
\rightarrow \mu^- + \pi^+ + n+ p$ and $\nu +d \rightarrow \mu^-+\pi^0+p+p$
reactions. The importance of including the $NN$ final state interactions to
understand the experimental data of these neutrino-deuteron reactions is
demonstrated. Our results strongly suggest that the spectator approximation
used in the previous analyses to extract the pion production cross sections on
the nucleon from the data on the deuteron is not valid for the $\nu + d
\rightarrow \mu^-+ \pi^+ +n+p$, but is a good approximation for $\nu + d
\rightarrow \mu^-+ \pi^0 + p+p$.
