In the ISS they obtain Oxygen from water through electrolysis. I guess this could be possible in Mars if they land near a large water source. NASA in the other hand, it's working for ways to obtain Oxygen from CO2, for using this method in their plans for going to Mars. Now, how about SpaceX? Is it known how does SpaceX plan to obtain Oxygen in Mars?
As far as I know, SpaceX plans to use a combination of Water mining and C0² collection because they have to produce Methane as well. But I could also imagine that they will use Plants etc. to generate Oxygen. Or that they will use CO² to generate Oxygen on its own like the MOXIE experiment on the Mars 2020 Rover will.