Yes, you can. In the mobile app, go to the ME screen and tap on the MOOD option at the top. You will see an "Export" icon in the upper right corner (next to the cog wheel "Settings" icon).
In the web version of the app, simply navigate to the ME page to find the "Export" icon in the upper right corner.
Tapping on "Export" icon will let you choose a report for this week or last week to send to yourself or someone else (like a family member or therapist).