How to exclude people with depression, or other mental illness from the group?

This has to be handled subtly. Since the first sitting involves only cleaning, you can make a gentle announcement and ask people on medication for anxiety / depression / mental illness etc. to contact a preceptor in person and decide what is to be done next.

If someone is already an abhyasi, and develops mental depression, you may ask them to meditate with you. Do not exclude them or leave them on their own. Clean them during sittings, and have them do their own prayer and cleaning, until the period of depression has lifted. They can also practise the Heartfulness Guided Relaxation every day and come to the local centre or ashram to help with volunteer work. [from BGP, p 49]