We present results of three-dimensional (3D), radiation-magnetohydrodynamics (MHD) simulations of core-collapse supernovae in full general relativity (GR) with spectral neutrino transport. In order to study the effects of progenitor's rotation and magnetic fields, we compute three models, where the precollapse rotation rate and magnetic fields are included parametrically to a 20 M$_{\odot}$ star... While we find no shock revival in our two non-magnetized models during our simulation times ($\sim500$ ms after bounce), the magnetorotationally (MR) driven shock expansion immediately initiates after bounce in our rapidly rotating and strongly magnetized model. We show that the expansion of the MR-driven flows toward the polar directions is predominantly driven by the magnetic pressure, whereas the shock expansion toward the equatorial direction is supported by neutrino heating. Our detailed analysis indicates that the growth of the so-called kink instability may hinder the collimation of jets, resulting in the formation of broader outflows. Furthermore we find a dipole emission of lepton number, only in the MR explosion model, whose asymmetry is consistent with the explosion morphology. Although it is similar to the lepton-number emission self-sustained asymmetry (LESA), our analysis shows that the dipole emission occurs not from the protoneutron star convection zone but from above the neutrino sphere indicating that it is not associated with the LESA. We also report several unique neutrino signatures, which are significantly dependent on both the time and the viewing angle, if observed, possibly providing a rich information regarding the onset of the MR-driven explosion. (read more)