Is it permissible to work temporarily as a teaching assistant in a mixed-gender university, with the aim of obtaining a master's degree whose costs the university covers and whose acquisition it expedites, along with the intention of minimizing evil, due to the need for the master's degree to open a clinic?

If you avoid prohibitions and enjoin against evil to the best of your ability, and you strive to minimize evil, then there is no objection to your undertaking this work to achieve benefits and reduce evils. For the Shari'ah came to achieve benefits and minimize harms, and what is prohibited as a deterrent (sadd al-dhari'ah) becomes permissible for an overriding benefit.