To send separate campaigns, simply make a duplicate of the campaign (there is a copy button). To segment your list, go into Mailing List Groups on the left menu and create a group and then go into Mailing List, and add specific recipients to that group. Then you can send the new campaign to that group. I would recommend you name the new copy of the campaign in a way that let's you know which segment / group the campaign is for. Also, make sure that you do not add the same recipient to multiple groups and then send the duplicated campaign to both groups. If you do this, they will get the same promo 2x. We usually prevent recipients from receiving the same promo more than once, but if you create duplicate campaigns, we cannot prevent it, so you must be careful.
Once the separate campaigns are created/duplicated we suggest renaming them to avoid confusion. To schedule different send times press send and you'll see a time & date option. Adjust the date & time and press save. Promo.ly will send your campaign the date you selected.