You're going to have to eat very cleanly to get and keep visible abs. The normal "high fat low carb" Primal will probably not do. You're going to have to do a high protein, lower fat, low-to-moderate carb version, most likely. You're going to have to eat maintenance calorie, low fat, high protein, moderate carb during lift days to maintain muscle and eat lower calorie, lower fat, high protein, lower carb during rest days to lose body fat.
If you don't lift heavy weights during your "cut," you will likely lose muscle mass at a similar rate to fat mass, so you'll never achieve the desired muscle definition with a calorie deficit. You'll just get skinny-fat. That's the troubling balance - to eat so well you can maintain a solid training program while on a calorie deficit. It's hard and takes dedication - which is why hardly anyone has visible abs in modern, developed socieities.