Bonnet,

Actually mass_mailing is dependent on module "website_mail" which is dependent on "website" module. So it means we can't use mass_mailing without "website" module. Ideally mass_mailing shouldn't be dependent on any website modules.

Possible Solution : Now If you don't want to show website pages then simply disable all Qweb views of "website" module.  We have no other way then this. Because website module must be installed in order to use module "mass_mailing". So for disable all "website" module's qweb views please go to setting >> Technical >> User Interface >> Views and find the Qweb views of website module. ( You can identify this from external ID ) Disable all of them by untick "Active" field. Also please remove the website pages from Settings >> Website Settings menu.

Update : In V9 they have separated mass_mailing and website_mass_mailing modules. But if you are using V8 then you have to deal with above way.