how to separate a mixture of sodium chloride and sodium hydroxide
One solution would be to reduce the amount of solvent (under vacuum for instance), then filter out the precipitated NaCl at high temperature (at higher temperatures NaOH has as much as &gt;10x the water solubility of NaCl).
The common ion effect will play in your favour, as the high water solubility of NaOH at higher temperatures will help you reach NaOH concentrations that strongly disfavours NaCl solubility.
The way to go may be to first reduce the solvent mass under vacuum at acceptably safe temperatures, and once the desired mass is reached redissolving most of the precipitated NaOH by pushing the temperature up before filtration to a level at which most NaOH has redissolved.
Use appropriate protection equipment and contact material to handle very hot NaOH.