Generally the fat attached to the skin removed is cut out

With a tummy tuck, there is skin removed. The fat that is attached to that skin is cut out with the skin. Sometimes, there is other fat in the upper abdomen or the flanks that is liposuctioned at the same time as the tummy tuck.

With abdominoplasty, whether a mini or full, my preference is to remove the fat from the central portion by directly cutting it out. Using liposuction on the part that is raised up as a flap may pose some additional risk, but it is commonly used on adjacent areas such as the waist or hips. By thinning the flap with direct removal of the fat, it gives a lot of control to the thickness and creates a surface for sutures called "progressive tension" which means less drainage (your drain can come out in a couple of days at the most) as well as good shaping and less tension along the skin closure, which contributes to good healing with minimal scar.

When performing a mini tummy tuck, it's important for the surgeon to not only address any excess fat that may be present, but also to evaluate the abdominal wall muscles as well as the quality and the amount of skin. In most cases I will directly excise the fat so as to precisely control the thickness of the skin and fat that remains, and then plicate or tighten the muscles of the abdomen before removing any excess skin that's present. You can achieve good results with liposuction of this area first, but the surgeon must be cautious so as to avoid damaging the blood supply to the skin, which could cause a delay in healing. In the end, a lot of this comes down to your particular anatomy as well as the preference of the surgeon, and either technique can create very nice results.