We present the results from XMM-Newton observations of the highly optically polarized broad absorption line quasar (BALQSO) CSO 755. By analyzing its X-ray spectrum with a total of ~3000 photons we find that this source has an X-ray continuum of `typical' radio-quiet quasars, with a photon index of Gamma=1.83^{+0.07}_{-0.06}, and a rather flat (X-ray bright) intrinsic optical-to-X-ray spectral slope of alpha_ox=-1.51. The source shows evidence for intrinsic absorption, and fitting the spectrum with a neutral-absorption model gives a column density of N_H~1.2x10^{22} cm^{-2}; this is among the lowest X-ray columns measured for BALQSOs. We do not detect, with high significance, any other absorption features in the X-ray spectrum. Upper limits we place on the rest-frame equivalent width of a neutral (ionized) Fe Ka line, <=180 eV (<=120 eV), and on the Compton-reflection component parameter, R<=0.2, suggest that most of the X-rays from the source are directly observed rather than being scattered or reflected; this is also supported by the relatively flat intrinsic alpha_ox we measure. The possibility that most of the X-ray flux is scattered due to the high level of UV-optical polarization is ruled out. Considering data for 46 BALQSOs from the literature, including CSO 755, we have found that the UV-optical continuum polarization level of BALQSOs is not correlated with any of their X-ray properties. A lack of significant short- and long-term X-ray flux variations in the source may be attributed to a large black-hole mass in CSO 755. We note that another luminous BALQSO, PG 2112+059, has both similar shallow C IV BALs and moderate X-ray absorption.