Jesus said, "Blessed are the pure in heart, for they shall see God" (Matthew 5:8). Jesus is the One who makes the heart pure. He has been purifying hearts for centuries. The One who spoke about being pure in heart, is the only One who can make the heart pure. Hearts are made pure through Christ our Lord.
"For with the heart one believes unto righteousness" (Romans 10:10). Believing on the Lord Jesus Christ is trusting Him to do in us, what we cannot do for ourselves. He is able to make us pure in heart. The righteousness of Christ is accounted to us by faith in Christ (2 Corinthians 5:21).
God's Spirit purifies the believer's heart based upon the sacrifice of Jesus Christ at the cross. "The blood of Jesus Christ His Son cleanses us from all sin" (1 John 1:7). There is no heart so sinful that Jesus cannot make pure. We may not be able to explain how Jesus purifies our hearts, but the shed blood of Jesus cleanses believers from every sin.
The blood of Jesus, through the power of the Holy Spirit, continues to cleanse the hearts of believers. The goal is to sin not, but when a believer sins, fresh cleansing is available. Confession of sin to God in prayer brings cleansing. "If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness" (1 John 1:9). The pure in heart are cleansed by the blood of Jesus.