Spinning cone column (SCC) distillation has been shown to be a commercially suitable technique for dealcoholized wine (DW) manufacturing, but there are not enough studies about its influence on the DW quality. So, the effect of this technique on the antioxidant activity (% of remaining 1,1-diphenyl-2-picrylhydrazyl radical) and the phenolic compound composition of red, rose, and white DW, obtained at pilot plant scale, has been analyzed. Nineteen raw wines (RWs) from different grape varieties and five different Spanish viticultural regions have been studied before and after dealcoholization. The total phenolic content, flavonols, tartaric esters, and anthocyanins, was determined by spectrophotometry, while the content of phenolic compounds such as stilbenes (trans- and cis-resveratrol), flavonols (rutin, quercetin, and myricetin), flavan-3-ols [(+)-catechin and (-)-epicatechin], anthocyanins (malvidin 3-glucoside), and non-flavonoids (gallic, caffeic, and p-coumaric acids) was determined by high-performance liquid chromatography (HPLC). The resveratrol contents in red wines were between 1.81 and 34.01 mg/L in RWs and between 2.12 and 39.57 mg/L in DWs, Merlot being the grape producing the RWs and DWs with higher resveratrol content. In general, the percent of remaining DPPH(*) was similar or slightly higher (until 5 units of % of remaining DPPH(*)) in DWs versus RWs. This small difference may be due to removal of SO2 (that is an antioxidant) from RWs during distillation. DWs and RWs show similar contents of the studied phenolic compounds, with a tendency, in some cases, to exhibit increases after dealcoholization, caused by the concentration effect via removal of the ethanol. From this work, we can deduce that SCC distillation is a dealcoholization technique minimally destructive with the wine phenolic compounds.