We do not currently support an option to hide your submissions from other students or mentors. This is due to the collaborative nature of design – we've found that students tend to have the most success when learning with and from others, and we use the platform to help facilitate that.
On the other hand, if you want to make your profile private so it is not searchable via search engines, you can go to your the settings tab of your profile, and scroll down to the box marked “set profile to private”.
Here’s a video showing you how. This will allow only people logged into a Designlab account to view your profile and work: