  We present our numerical results of two-dimensional magnetohydrodynamic (MHD)
simulations of the collapse of rotating massive stars in light of the collapsar
model of gamma-ray bursts (GRBs). Pushed by recent evolution calculations of
GRB progenitors, we focus on lower angular momentum of the central core than
the ones taken mostly in previous studies. By performing special relativistic
simulations including both realistic equation of state and neutrino coolings,
we follow a unprecedentedly long-term evolution of the slowly rotating
collapsars up to $\sim$ 10 s, accompanied by the formation of jets and
accretion disks. Our results show that for the GRB progenitors to function as
collapsars, there is a critical initial angular momentum, below which matter is
quickly swallowed to the central objects, no accretion disks and no MHD
outflows are formed. When larger than the criteria, we find the launch of the
MHD jets in the following two ways. For models with stronger initial magnetic
fields, the magnetic pressure amplified inside the accretion disk can drive the
MHD outflows, which makes the strong magnetic explosions like a 'magnetic
tower' (type II). For the models with weaker initial magnetic fields, the
magnetic tower stalls first and the subsequent MHD outflows are produced by
some eventual inflows of the accreting material from the equator to the polar
regions (type I). Regardless of type I or II, the jets can attain only mildly
relativistic speeds with the explosion energy less than $10^{49} \erg$, which
could possibly be related to the X-ray flashes. Due to high opacity for
neutrinos inside the disk, we find that the luminosities of $\nu_e$ and
$\bar{\nu}_e$ become almost comparable, which is advantageous for making the
energy deposition rate larger.
