  We investigate the total decay rate of the (ground state) $B_c$ meson within
the framework of the relativistic constituent quark model formulated on the
light-front (LF). The exclusive semileptonic (SL) and nonleptonic (NL) beauty
and charm decays of the $B_c$ meson are described through vector and axial
hadronic form factors, which are calculated in terms of the overlap of the
parent and daughter LF wave functions. The latters are derived via the
Hamiltonian LF formalism using as input the update version of the ISGW model.
The inclusive SL and NL partial rates are calculated within a convolution
approach inspired by the partonic model and involving the same $B_c$ wave
function which is used for evaluation of the exclusive modes. We predict the
partial rates for 74 exclusive SL and NL channels and 43 inclusive partial
rates corresponding to the underlying $\bar{b}\to \bar{c}$ and $c\to s$ quark
decays. Based on our approach we find $\Gamma^{\bar{b}}(B_c)= 0.52 \pm 0.02
ps^{-1}$, $\Gamma^{c}(B_c)= 0.98 \pm 0.07 ps^{-1}$, where the theoretical
uncertainty is dominated by the uncertainty in the choice of the threshold
values at which the hadron continuum starts. For the $B_c$ lifetime we obtain
$\tau_{B_c}= 0.63 \pm 0.02 ps$ in a good agreement with the prediction obtained
using the nonrelativistic operator product expansion. We also predict decay
rates for many specific weak transitions of $B_c$. In particular, for the
branching fractions of the $B^+_c \to J/\psi\mu^+\nu_{\mu}$, $B_c^+\to
J/\psi\pi^+$ and $B_c^+ \to J/\psi+X $ decays we obtain 1.7%, 0.1 % and 13.2%,
respectively.
