Shall I mimic someone's bad behavior to someone to make them see what they are like or is that God's issue?

No, it's not permitted to mimic someone's bad behavior to show them what they're like. That's playing a dangerous game and it's not our job. Listen, when you mimic bad behavior, even with good intentions, what happens? You're becoming that bad behavior, even if temporarily. The yetzer hara works little by little - it trains you to become like him. When you start acting out in any way, even to make a point, you're opening a door that's very difficult to close. You think you're just pretending, but your neshama doesn't know the difference. You're programming yourself. The Chazon Ish teaches us that when we act in a certain way repeatedly, it actually changes us - not just spiritually, but it leaves a mark on our soul and even affects our physical form and character. If you're mimicking disgusting behavior or bad middot to teach someone a lesson, you're poisoning yourself in the process. What you should do instead is rebuke them properly - privately first, with respect, telling them directly what they're doing wrong according to the Torah. If they don't listen after private rebuke, and they're violating Torah publicly, then in certain cases you may need to address it more directly, but never by becoming like them yourself. You warn them, you teach them, you guide them - but you don't imitate their sins. Hashem runs the world measure for measure. If someone needs to learn a lesson about their behavior, Hashem will teach them. That's His job, not yours. Your job is to speak truth, to rebuke according to halacha, and to protect yourself and others from bad influences - not to become the bad influence yourself, even for a moment.