Removal of sin
Jesus didn't actually "disappear" or erase anyone's sin. He paid the penalty for it. The sin was still in effect and he took the punishment that was due to us. Because he was sinless, he was able to pay the penalty for us. Therefore, sin has no hold or claim on those who accept the gift of God's freedom.
Although God's grace does cover any and all sins that a person might commit, that doesn't give a person license to do as they please.
"So what do we do, then? Do we persist in sin so that God’s kindness and grace will increase? What a terrible thought! We have died to sin once and for all, as a dead man passes away from this life. So how could we live under sin’s rule a moment longer?" [The Passion Translation]
Relationship vs Contract
Some people think that God is like a genie; that you can do whatever you like as long as you fulfill certain contract obligations. If you say so many prayers, or if you do specific things, that you'll be able to do as you please. Those who believe so have missed the point. It's not about technicalities, it's relational.
Jesus didn't die so we could get blessed if we did specific things to unlock specific rewards. He died that we could live in relationship with him. When we realize that he loves us and when we truly love him, we don't want to hurt him. Since sin separates us from him and hurts him, we begin to no longer sin as we don't want to cause him pain. Additionally, it causes us pain to be apart from him, and that hurts us. In order to stop hurting ourselves and the One we love, we stop pursuing sinful desires.
tl;dr Yes, we can keep sinning, but because our hearts become changed, we no longer want to sin when we truly enter a relationship with Jesus.
Romans 6 source: https://www.biblegateway.com/passage/?search=Romans+6&version=TPT
Jesus Christ didn't die to disappear the sins of man but to redeem man from sin. He paid the price for man's sins by giving himself for the sins of man. This implies that anyone that believes in Jesus Christ and resolves in his or her heart to live for God through Jesus Christ will be saved
Christ didn't die for our sins to give us the freedom to continue sinning but to deliver us from sin and it's consequences and enable us to live holy lives unto God.
Anyone that refuses to accept the finished work of Christ on the cross and make a resolve to live for God through Christ will be condemned to eternal damnation when christ comes again.