imo, when cutting, it should be a very slow process where you gradually cut out carbs from your diet while gradually decreasing your calorie intake to end up in a deficit
lots of people cut too fast (i've made this mistake myself several times) and end up losing a lot of weight, but a lot of muscle too, and therefore a lot of strength
my advice would be to find your maintenance number and start by cutting only 200 calories from that and see how you progress. If you end up stalling for a few weeks, cut down 200 more calories. No need to lose 15 pounds in a month, you'll lose much more months of training