From MMA Tycoon Help
Much like injuries, cuts will only occur during a fight in MMA Tycoon and cannot happen during training. This is just to avoid people's fun being ruined by constantly getting fights re-arranged due to training injuries and cuts.
If your fighter is cut, he may still be allowed to fight but the cut may open up more easily in the next fight and can cause the fighter to lose by TKO (cuts).
If your fighter's cut is worse than 20 days, he will automatically lose by TKO due to cuts, so it goes without saying that you should not book a fighter for a fight with a serious cut because it will mean an automatic TKO loss.