The Aramaic can be translated, “be renewed by the Spirit, that is your thinking [should be renewed].”
If we put off the “old man”, then our thinking starts to be renewed by God who is the Spirit.
It makes sense to see that the mind begins to be renewed by God and we grab a hold of it, then that makes us want to change. You could better translate it, be renewed in [your thinking] by the Spirit. There is an ellipsis in the verse then, which implies that your thinking is what should be renewed.
With God’s help is how we change our minds or thinking. Sometimes it is very difficult to change certain habit patterns of thinking. The word, “put off” means to strip off, put away from. It would be like when you have dirty clothes on and want to get them off very quickly so that you can take a shower. The old man is corrupt because it is led away by the deceitful desires of the flesh. So strip it off! Allow the Spirit to teach your mind what is the true and godly way to live and don’t allow the flesh to have authority over our minds. This is the beginning of the “renewed mind”.