  The spin-boson model has nontrivial quantum phase transitions at zero
temperature induced by the spin-boson coupling. The bosonic numerical
renormalization group (BNRG) study of the critical exponents $\beta$ and
$\delta$ of this model is hampered by the effects of boson Hilbert space
truncation. Here we analyze the mean-field spin boson model to figure out the
scaling behavior of magnetization under the cutoff of boson states $N_{b}$. We
find that the truncation is a strong relevant operator with respect to the
Gaussian fixed point in $0<s<1/2$ and incurs the deviation of the exponents
from the classical values. The magnetization at zero bias near the critical
point is described by a generalized homogeneous function (GHF) of two variables
$\tau=\alpha-\alpha_{c}$ and $x=1/N_{b}$. The universal function has a
double-power form and the powers are obtained analytically as well as
numerically. Similarly, $m(\alpha=\alpha_{c})$ is found to be a GHF of
$\epsilon$ and $x$. In the regime $s>1/2$, the truncation produces no effect.
Implications of these findings to the BNRG study are discussed.
