How do I 'cut-up'?

Brighton,

You're obviously no stranger to lifting heavy weights so now that you're looking to cut then you need to look at your dietary macro ratios of protein:carbs:fats and adjust accordingly. Keep your protein:carb intake around your workouts at a 1:2 but reduce your carbs thoughtout the day. OK so your calories in - Try and aim for 13 cals per lb of bodyweight as a general rule.

Reducing carbs - if your current carb intake is around 300g a day, reduce to 150g and see how you get on. If after a week or two you feel like you're not making the progress reduce your carbs again by around 50g but as you'll already be in calorie deficit(after cutting your carbs in half) replace your cals with a lean protein source. If you can, keep your carbs to breakfast and peri-workout and for your other meals stick to lean protein sources and plenty of green veg. Snack on berries, a few nuts now and again and whey protein shakes.

Keep your fat intake at around 0.5g per lb of body weight, keep your protein high at around 1.5g per lb of bodyweight. Introduce some HIIT training twice a week after a workout, preferably on a non leg training day but it's a matter of personal preference and intensity.

Without seeing your workouts I couldn't really comment but you can adapt your workouts to benefit your metabolism by shortening rest times and reducing the weight by around 5 - 10% - Hammering out the same weight with a shorter rest may lead to central nervous system fatigue so reduce the rest, reduce the weight.
Although some people say that walking does very little to "burn" fat it's not so much fat that you need to worry about as calories burned so as a small bonus get as much NEPA or Non Exercise Physical Activity such as walking on your rest days.