According to Ramayana, Lakshmana cut off the nose of Shurpanakha. But how and where did Shurpanakha lose her nose?
This is mentioned in Valmiki Ramaya Aranya Khanda.
When Rama, Sita and Lakshamana were staying in parNa shaala, straw-cottage in Panchavati, nearby river Godavari in Dandakaranya (present day Nashik), Shuurpanakha approached Rama with lust. Rama averts her saying that his brother was young and unmarried and suggested to woo him (pun intended).
When Shuurpanakha approached Lakshmana, he told her that he was just a servant to his brother Rama and suggested her to become the younger wife of Rama (Lakshmana was also punning). After listening to Lakshamana's words, which she thought to be true,she went to Rama who was sitting with Sita in the cottage and decided to eat Sita.
अद्य इमाम् भक्षयिष्यामि पश्यतः तव मानुषीम् |
त्वया सह चरिष्यामि निःसपत्ना यथा सुखम् || ३-१८-१६
"Now I wish to eat up this human female right before your very eyes, and then I can blithely make merry along with you, without the botheration of a co-wife." Said Shuurpanakha to Rama. [3-18-16]
ताम् मृत्यु पाश प्रतिमाम् आपतंतीम् महाबलः |
विगृह्य रामः कुपितः ततो लक्ष्मणम् अब्रवीत् || ३-१८-१८
By that the great-energetic Rama took umbrage and checking her who is like the noose of death swooping down on Seetha said to Lakshmana. [3-18-18]
क्रूरैः अनार्यैः सौमित्रे परिहासः कथंचन |
न कार्यः पश्य वैदेहीम् कथंचित् सौम्य जीवतीम् || ३-१८-१९
"Punning in any way with the base and brutish is inapposite, oh, gentle Saumitri, mark note of Vaidehi, somehow surviving [3-18-19]
इमाम् विरूपाम् असतीम् अतिमत्ताम् महोदरीम् |
राक्षसीम् पुरुषव्याघ्र विरूपयितुम् अर्हसि || ३-१८-२०
"She is freakish, knavish and overtly ruttish, oh, tigerly man, it will be apt of you to deface this paunchy demoness " Thus Rama said to Lakshmana. [3-18-20]
इति उक्तो लक्ष्मणः तस्याः क्रुद्धो रामस्य पश्यतः |
उद्धृत्य खड्गम् चिच्छ्हेद कर्ण नासम् महाबलः || ३-१८-२१
Thus said to that mighty Lakshmana he infuriately drew sword and chopped off her ears and nose before the very eyes of Rama. [3-18-21]
निकृत्त कर्ण नासा तु विस्वरम् सा विनद्य च |
यथा आगतम् प्रदुद्राव घोरा शूर्पणखा वनम् || ३-१८-२२
On hewing off her ears and nose she that ghastly Shuurpanakha blared highly and discordantly, and very speedily fled into forest as she came. [3-18-22]