That phrase is taken from John Owen's classic work, "The Mortification of Sin." Mortification means to put to death, and foundational to his book is Romans 8:13 - "For if you live according to the flesh you will die, but if by the Spirit you put to death the deeds of the body, you will live."
John Owen was an ardent defender of justification by faith alone, but he was also passionate for holiness and communion with God and realized that sin was the greatest problem to these. As he said himself: "Sin sets its strength against every act of holiness, and against every degree we grow to. Let not that man think he makes any progress in holiness who walks not over the bellies of his lusts. He who does not kill sin in this way takes no steps towards his journey’s end." John Owen rightly continues on how we should take an aggressive stand against sin since it will be with the believer his whole life. It may not have us enslaved but until Christ returns it always "seduces, entices, fights, rebels" as long as we are on earth. So a man must "keep a diligent watch over his heart, its root and fountain" all the days of his life.
With that in mind, let me give you some ammunition in your battle against sin and fight for joy in the Lord. Here is some excellent advice from John Owen:
"Be much in thoughtfulness of the excellency of the majesty of God and thine infinite, inconceivable distance from him. Many thoughts of it cannot but fill thee with a sense of thine own vileness, which strikes deep at the root of any indwelling sin. When Job comes to a clear discovery of the greatness and the excellency of God, he is filled with self-abhorrence and is pressed to humiliation, Job 42: 5, 6. And in what state does the prophet Habakkuk affirm himself to be cast, upon the apprehension of the majesty of God? chap. 3:16. “With God,” says Job, “is terrible majesty.” Job 37:22. Hence were the thoughts of them of old, that when they had seen God they should die. The Scripture abounds in this self-abasing consideration, comparing the men of the earth to “grasshoppers,” to “vanity,” the “dust of the balance,” in respect of God. Isaiah 40:12–25. Be much in thoughts of this nature, to abase the pride of thy heart, and to keep thy soul humble within thee. There is nothing will render thee a greater indisposition to be imposed on by the deceits of sin than such a frame of heart. Think greatly of the greatness of God."