One of the biggest problems with the use of traditional fining agents is that some of them present allergenic characteristics or are not suitable for vegan consumers due to their animal origin. An alternative to these traditional proteinaceous agents could be cell walls from grape pulp. This material could be used to modify the final phenolic concentration of a wine due to its affinity for phenolic compounds. In this study, the ability of freeze-dried grape pulp fiber, rich in pulp cell walls, to act as a fining agent was analyzed in wines from three different varieties: Cabernet Sauvignon, Syrah, and Monastrell. After the use of this material, the wine chromatic characteristics and total tannin concentration were analyzed by spectrophotometric and chromatographic techniques. In addition, the wines were contaminated with ochratoxin A and histamine to check whether this material could also be a tool for removing these wine contaminants. The pulp fiber presented a high capacity to retain phenolic compounds, especially tannins; however, there were differences depending on the studied wine. The largest reduction in tannin concentration after fining was observed when this material was used in Cabernet Sauvignon wines (23%), whereas for Monastrell wines the reduction was lower (18.3%) and even lower for Syrah wines (14.3%). This fining agent also reduced the anthocyanin concentration of the three red wines, although to a lesser extent than the reduction observed for tannins. A really interesting result was that the addition of this fining agent reduced the concentration of ochratoxin A by 50% in all the studied wines.