Many people have misunderstanding about Tasawwuf or Sufism, thinking it is something beyond the Quran and Hadith/Sunnah. This has happened due to the fact that some Ulama & Muftis (Scholars) of Islam has shunned and claimed the path of Tasawwuf to be bid’ah (innovation) while those who have taken the garb of Sufis (tasawwuf experts) do not give importance to the Shariah i.e. Quran and Hadith/Sunnah, as they’re supposed to.
Tasawwuf is not an innovation and did exist at the time of Prophet Muhammad ﷺ just like all other practices within Islam, however the term itself did not exist, it was a later development. For instance the term Usul Al Fiqh which means "Islamic Jurisprudence" is a science on the practice of Islamic rules and regulations that existed at the time of Prophet Muhammad ﷺ but the term did not exist. The Sahabas (Prophet's companions) did not refer to this knowledge as Usul Al Fiqh as we know it. The necessity of Usul Al Fiqh is extremely important as it has guided Muslims through centuries of how to practice rules and regulations of Islam in their daily lives. The scholars of the later centuries developed this science further as there was continuous need of it and therefore this term came to be. Another example is the Ilm Al hadith meaning "sciences of hadith". The hadith were being collected at the time of Prophet ﷺ but the science and methodology of collection did not exist till many decades after him. As Islam spread and companions went to different parts of the world to preach, hadith were written by those who enjoyed their company. Then came the requirement for a process that would distinguish authentic from the weak and fabricated hadith, hence the subject of Ilm al hadith came to exist.
Tasawwuf means (Islamic) science of gaining purity to attain spirituality, this is simply because we are not just Ruh (spirit) and neither are we just physical body, we are both. Gaining purity will help increase one’s spirituality, which is the heart of Islam because the main purpose of our creation is to gain communion with our Creator, Allah ﷻ, which can only be fulfilled through the medium of our hearts, as Allah ﷻ reminds: “Verily, he who has purified the heart is successsful and he who had despoiled it has lost.” (Al Quran 91:9–10). The Prophet ﷺ also said “There is one piece of flesh in the body which if it is good, the whole body will be good and if it is ruined then the entire body is ruined, and that piece is the heart.” (Hadith)
Tasawwuf is an internal enlightenment that can only be attained through the medium of our hearts but the process for it begins by following obligatory external rulings which fall within the sphere of Shariah (sacred law) such as Salaah (5 daily prayers), Zakah (obligatory charity), Fasting (30 days in Ramadaan), and other necessary acts according to the Sunnah (way) of Prophet Muhammad ﷺ. Just as there are topics within the Quran and the books of Hadith/Sunnah that teach external acts on Salaah, Zakah, rules on marriage and divorce, trading and commerce, they also include chapters on internal acts on how to control one’s anger, how to behave righteously and maintain a good character, preventing Riya (showing off), purifying one’s heart of jealousy & malice, keep a check on one’s lust (nafs) & ability to indulge in unnecessary arguments. Tasawwuf primarily focuses on perfecting these internal acts, and historically Sufis are those Islamic saints that perfected those characteristics within themselves and became examples for other to follow. Hence it is the external and internal Islamic obligations combined within individuals that assist in attaining spirituality in Islam called Tasawwuf. Very importantly Imam Malik (r.a), one of the greatest Imams in the history of Islam said: “He who practices Tasawwuf without learning Sacred Law (Shariah) corrupts his faith, while he who learns Sacred Law (Shariah) without practicing Tasawwuf corrupts himself. Only he who combines the two proves true.”
 It is related by the muhaddith Ahmad Zarruq (d. 899), the hafiz `Ali al-Qari al-Harawi (d. 1014), the muhaddiths `Ali ibn Ahmad al `Adawi (d. 1190) and Ibn `Ajiba (d. 1224), and others - http://sunnah.org/tasawwuf/scholar4.htm#2