Multimode fibers are attractive for high-power lasers if transverse modes are efficiently controlled. Here, a dielectric thin-film mirror (R~20%) is micro-fabricated on the central area of the end face of a 1 km multimode 100/140 µm graded-index fiber and tested as the output mirror of a Raman laser with highly multimode (M2~34) 940 nm diode pumping. In the cavity with highly reflective input FBG, Raman lasing of the Stokes wave at 976 nm starts at the threshold pump power of ~80 W. Mode-selective properties of mirrors with various diameters were tested experimentally and compared with calculations in COMSOL, with the optimum diameter found to be around 12 µm. The measured Raman laser output beam at 976 nm has a quality factor of M2~2 near the threshold, which confirms a rather good selection of the fundamental transverse mode. The power scaling capabilities, together with a more detailed characterization of the output beam's spatial profile, spectrum, and their stability, are performed. An approximately 35 W output power with an approximately 60% slope efficiency and a narrow spectrum has been demonstrated at the expense of a slight worsening of beam quality to M2~3 without any sign of mirror degradation at the achieved intensity of >30 MW/cm2. Further power scaling of such lasers as well as the application of the proposed technique in high-power fiber lasers are discussed.