The problem with a circuit training using sledge hammer and tires is the lack of progression. How do you go up in weights? You can only do more reps which then becomes more endurance training.
And the faster you move between sets., the less your strength is. But that’s the compromise.
You can work on conditioning on another day like Karky mentioned. Sledge pull, uphill walk are good for conditioning. And you can keep your regular workout rest time shorter and move fast between sets. Or just one day per week do all the functional stuff like tire flip, sledge hammer and such. In strongman training, some do just one day for strongman event training and the rest of the days are regular weight room workouts.