We have discovered a new rapidly oscillating Ap (roAp) star among the Kepler mission target stars, KIC 10195926. This star shows two pulsation modes with periods that are amongst the longest known for roAp stars at 17.1 and 18.1 min, indicating that the star is near the terminal-age main sequence. The principal pulsation mode is an oblique dipole mode that shows a rotationally split frequency septuplet that provides information on the geometry of the mode. The secondary mode also appears to be a dipole mode with a rotationally split triplet, but we are able to show within the improved oblique pulsator model that these two modes cannot have the same axis of pulsation. This is the first time for any pulsating star that evidence has been found for separate pulsation axes for different modes. The two modes are separated in frequency by 55 μHz, which we model as the large separation. The star is an α2 CVn spotted magnetic variable that shows a complex rotational light variation with a period of Prot= 5.684 59 d. For the first time for any spotted magnetic star of the upper main sequence, we find clear evidence of light variation with a period of twice the rotation period, that is, a subharmonic frequency of νrot/2. We propose that this and other subharmonics are the first observed manifestation of torsional modes in an roAp star. From high-resolution spectra, we determine Teff= 7400 K, log g= 3.6 and v sin i= 21 km s-1. We have found a magnetic pulsation model with fundamental parameters close to these values that reproduces the rotational variations of the two obliquely pulsating modes with different pulsation axes. The star shows overabundances of the rare earth elements, but these are not as extreme as most other roAp stars. The spectrum is variable with rotation, indicating surface abundance patches.