We present spectroscopic observations of the black hole binary V4641 Sagittarii, obtained between 2004 July 4 and 2005 March 28, which cover the minor outburst of the star in early 2004 July and quiescence variations on 19 nights scattered over six months. During the outburst, the star peaked approximately 3 mag brighter than usual, and our spectra were dominated by broad hydrogen, helium and iron emission lines. The very first spectra showed P Cygni profiles, which disappeared within a few hours, indicating rapid changes in matter ejection. The Hα line had multiple components, one being a broad blueshifted wing exceeding 5000 km s-1. During a simultaneously observed 10-min photometric flare up, the equivalent width of the Hα line temporarily decreased, implying that it was a flare of the continuum. The overall spectral appearance was similar to that observed in the 1999 September active phase, which suggests that similar mass-ejection processes were associated with both eruptions. In quiescence, the spectra were those of the early-type secondary star showing its orbital motion around the primary. By measuring cross-correlation radial velocities, we give an improved set of spectroscopic elements. Whereas we measure the same velocity amplitude (K2= 211.3 +/- 1.0 km s-1), within errors, as Orosz et al., our centre-of-mass velocity (γ= 72.7 +/- 3.3 km s-1) differs significantly from the previously published value (107.4 +/- 2.9 km s-1). However, we find evidence that the difference is caused by a systematic error in data reduction in the previous study, rather than by gravitational effects of an invisible third component.