You should be able to do the exact same thing in SplendidCRM. You can perform the same advanced search, and you can check the boxes and then click the Delete button that is at the bottom of the list of leads.

The checkboxes should already be there. However, in our recent releases, we have added the ability to enable/disable mass update. You may want to check the Modules editor in the Admin area to see if Mass Update has been disabled for the Leads module.