You can Perform dilutions of the culture to reduce population density, then re-isolate single colonies of algae under sterile conditions and agar streaking to separate species into distinct colonies is best way.

Dear Samaneah,

Appart from the commented by Shalini above, I recommend you look into:

-Micromanipulation

-Sucrose/percoll gradients and density centrifugation

Micromanipulation should be as resource and time consuming as colony and agar streaking, however sucrose/percoll separation could be faster. It depends on the cell size/density difference (and intraspecies variability) between your species.

In relation to contamination the answer is even more complicated. Algal cultures are typically never axenic. This is because a lot of microalgal species live symbiotically with other microorganisms (I believe mainly bacteria). As such, you need to have a clear purpose for which you want an axenic culture. Regardless, the safest bets are re-culturing and testing a variety of antibiotics.

In general, any type of question in this field tends to be answered by the excellent review by:

S.F. Valenzuela, et al., Isolation and Culturing Axenic Microalgae: Mini–Review, 2021, The Open Microbiology Journal

You can try sorting with FACS technique if there is a huge difference in cells characteristics mainly the cell size :)