A: Mortification and ascesis are usually mentioned in the same writings about mortification, so I will quote the Catholic sources on both here.

• Paragraph 1734, P. 430: "Freedom makes man responsible for his acts to the extent that they are voluntary. Progress in virtue, knowledge of the good, and ascesis enhance the mastery of the will over its acts."
• Paragraph 2015, P. 488: "The way of perfection passes by way of the cross. There is no holiness without renunciation and spiritual battle. Spiritual progress entails the ascesis and mortification that gradually lead to living in the peace and joy of the Beatitudes: He who climbs never stops going from beginning to beginning, through beginnings that have no end. He never stops desiring what he already knows - Homily of St. Gregory of Nyssa."
• Paragraph 2340, P. 562: "Whoever wants to remain faithful to his baptismal promises and resist temptations will want to adopt the means for doing so: self-knowledge, practice of ascesis adapted to the situations that confront him, obedience to God's commandments, exercise of the moral virtues, and fidelity to prayer: Indeed it is through chastity that we are gathered together and led back to the unity from which we were fragmented into multiplicity - St. Augustine."

• P. 1183, "1 Cor. 25-27: And everyone in a contest abstains from all things - and they indeed to receive a perishable crown, but we an imperishable. I, therefore, so run as not without a purpose; I so fight as not beating the air; but I chastise my body and bring it into subjection, lest perhaps after preaching to others I myself should be rejected."
• P. 1205, "Gal. 5:214: And they who belong to Christ have crucified their flesh with its passions and desires."
• P. 1318 "Ascetics: (1) The study embracing all of the theology of virtue and perfection and the means of gaining that perfection. (2) Those persons who apply the principles and teachings of ascetical theology; those using the practical means to acquire virtue and become perfect in order to achieve sanctity."
• P. 1368 "Mortification: Acts of fasting or self-imposed corporal punishments performed for a pious intention and for the spiritual good of the soul. It is a means of overcoming or weakening evil inclinations or overcoming anything that retards growth in the love of God and of neighbor."

• P. 106, "Asceticism: A form or rule of life accepted by an individual as one struggles toward Christian perfection. The scriptural basis for ascetical practices is in the command to avoid the concupiscence of the flesh, of the eyes and of the pride of life (1 John 2:16). Asceticism is a disciplinary tool that puts order and harmony in the soul, expiates for sins and enables one to imitate the sacrificial life of Christ. It springs from God and seeks to overcome obstacles to union with God. Central to ascetical practices is the understanding that these practices and the negation of the self they bring about are necessary for growth in Christ.

  There are two sides to ascetical theology, denying oneself and following Christ. The former calls for fasting, watchfulness, chastity, and self-discipline; these are seen as the means of purifying the soul from its passions and are the necessary means of growing in love of God.

  In the beginning of the modern era, there was a strong reaction against asceticism by the Reformers and Renaissance humanists. However, modern ascetics such as the Jesuits, Visitandines, some Puritans and some other modern Catholics adopted a more private and individual asceticism, and after Trent it was still widely practiced. Protestants such as the Puritans adopted a rigorous and negative asceticism, while Methodists have practiced a particularly modern form of asceticism. Asceticism has grown even further with the emergence of monastic communities in the Anglican and Lutheran Communions."

• P. 688, "Mortification: The free and deliberate self-imposition of forms of suffering, pain or self-denial, in order to suppress immoral and sinful inclinations, thereby drawing closer to God and increasing one's holiness of life. Acts of mortification are acts in which the person turns against sinful tendencies and toward God as our security against them. Mortifying acts are part of our Christian life, for they enable us to participate vicariously in the sufferings of Christ: 'Whoever wishes to be my follower must deny his very self' (Luke 9:23).

  Mortification brings about a detachment from material and bodily goods, and it implies a deepened attachment to spiritual goods and higher moral values. Mortification turns the person to seek the joy that is related to charity, fraternal love and discipleship with Christ. Mortification is important because it gives us an awareness of the ever-present nature of sin. It conditions us to be able to bear the burdens of Christian life in the world, by striving for the salvation of the world and the building of the kingdom. It promotes the virtue of penance, by which we call upon God for His grace to make us strong in our weakness."

Lastly, I have read other answers on the topic of mortification written by priest-experts on the subject. Their advice has been that Holy Church still believes in the practice of mortification. However, the anticipated mortification(s) should be discussed beforehand with one's confessor and the confessor's advice must be strictly adhered to (my emphasis). Remember, a confessor is acting in the person of Christ so the advise he is giving you is the advise of our Lord!