Pizza delivery and carryout locations servicing MesillaNew-Mexico can be found here. Find delivery menus, coupons, driving directions, maps, photos, and more for Mesilla pizza restaurants. Order pizza online or by phone from Mesilla pizza locations, with free take out or delivery options available. pizza locations have carryout and may have delivery available. Pizza in the 88046, among others in Mesilla, is a breeze with this service.