The purpose of saying a Mantra over and over is to empty one’s mind of all thoughts. The purpose of the Jesus Prayer is to fill our mind with the meaning of the words and to raise up our thoughts to God.
St. Paul teaches us to Rejoice always, pray without ceasing, in everything give thanks; for this is the will of God in Christ Jesus for you (1 Thessalonians 5:16-18).
This prayer of the heart is what Jesus helps us to achieve. The words of the Jesus Prayer are not magical; rather the words, practice and purpose of the Jesus Prayer are deeply biblical (cf. Luke 18:30).