I have a mixture of HNO₃ (aq), H₂C₂O₄ (aq) (oxalic acid) and H₂O. Is there anyway to remove oxalic acid from the other two components to produce two products oxalic acid (S) and HNO₃/H₂O mixture?

You already have oxalic acid. Cannot separate acid form as oxalic acid is very soluble in water. You could possibly try to convert the oxalate into a precipitate but that may well remove the nitrate too. Converting into Nitrate salts won't work since they are all very water soluble. Calcium oxalate is insoluble, work on that end.