The Word Sufism is an english word, in our Deen we only use arabic to describe the Deen, the word in Arabic for Sufism is Tasawwuf, and the act you perform is called Tazkiyah an Nafs, purifying your self of evil and bad while promoting good qualities in your self, and what you try to achieve by it is Ihsan, Human Perfection.
1) Surah Shams, 91:9 Allah takes an oath in the Quran like no other and swears by the act of Tasawwuf, “Qad Aflaha man Zakaha” (Zakaha = Tazkiya an nafs), “He Who Purifies it succeeds”, This is talking about getting rid of your bad qualities, Tazkiya Nafs.
2) Surah Abbasa, 80:3 The Blind Man comes to the Prophet (saws) seeking Islam and the Prophet (saws) frowns upon Him as his attention is elsewhere, Allah responds by Saying, “Wama yudrika La-alahu Yazaka” (Yazaka = Tazkiyah an Nafs), “Yet for all that didn't know, [O Muhammad,] he might perhaps have grown in purity”, So in Surah al Shams Allah mentioned the first part of Tazkiyah an Nafs and that is Purifying your self of Evil, In Surah Abbasa he mentions the second part, learning and Promoting Good qualaties in your character and growing as a person.
3) Surah Ashurah, 26:88-89, Allah says, “The Day whereon neither wealth nor sons will avail, But only he (will prosper) that brings to Allah a sound heart”, “a heart free of sins and love for this worldly life” (Tanwir al miqbas Min Tafsir Ibn Abbas). You Have to know the Acts of Tazkiyah Nafs to Free your Heart from Sin and love for this Dunya (world), and Only One science in islam deals with this Subject in all of islams history and that is Tasawwuf, Fiqh does not cover Human Character and Psychology, it covers the Fiqh of Halal and Haram, how to actually change your self, the ullumah deal with that in a different science of islam.
4) The most famous Hadith in all of Islam is the hadith of Jibril (hs), which occurred 86 days before the prophets (saws) death, it defines all the parts of Islam without a Doubt, into Fiqh (Islam), Aqeedah (Iman), Ihsan (Tasawwuf) and the Sings of the Hour.
Assalam o Alikum