We present optical spectroscopic follow-up of a sample of Distant Red Galaxies (DRGs) with K < 22.5 (Vega), selected by J-K > 2.3, in the Hubble Deep Field South, the MS 1054-03 field, and the Chandra Deep Field South. Spectroscopic redshifts were obtained for 15 DRGs. Only 2 out of 15 DRGs are located at z < 2, suggesting a high efficiency to select high-redshift sources. From other spectroscopic surveys in the CDFS targeting intermediate to high redshift populations selected with different criteria, we find spectroscopic redshifts for a further 30 DRGs. We use the sample of spectroscopically confirmed DRGs to establish the high quality (scatter in Delta z/(1+z) of ~ 0.05) of their photometric redshifts in the considered deep fields, as derived with EAZY (Brammer et al. 2008). Combining the spectroscopic and photometric redshifts, we find that 74% of DRGs with K < 22.5 lie at z > 2. The combined spectroscopic and photometric sample is used to analyze the distinct intrinsic and observed properties of DRGs at z < 2 and z > 2. In our photometric sample to K < 22.5, low-redshift DRGs are brighter in K than high-redshift DRGs by 0.7 mag, and more extincted by 1.2 mag in Av. Our analysis shows that the DRG criterion selects galaxies with different properties at different redshifts. Such biases can be largely avoided by selecting galaxies based on their rest-frame properties, which requires very good multi-band photometry and high quality photometric redshifts.
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