Contributors with "Site Owner", "Administrator" or "Store Manager" receive automated email notifications from Squarespace about Orders and Donations. If you've added someone with these permissions, you cannot control whether they receive these emails. However, they can choose to enable or disable them on a site-by-site basis from their account page.
To do this, they can visit their profile page and then click on Notifications. There are options for each site they contribute to. For more information, see Editing your contributor profile.