Scottish artist Craigie Aitchison, who was known for his aversion to self-promotion, cut the portrait after a visitor to his studio said it made him look good.
However, he was later persuaded by the National Gallery's head of conservation Martin Wyld to let him restore it, with the lacerations still visible.
The painting remained in the artist's possession until his death in 2009 and the National Portrait Gallery has now bought it, with funding from the likes of fashion designer Sir Paul Smith and Terence and Angela Danziger Miles.
Paul Moorhouse, the gallery's curator of 20th-century portraits, said: "Craigie Aitchison was a highly distinctive artist whose singular vision was rooted in an acute sensitivity to colour and subtle implications of meaning.
"We are delighted that this fascinating self-portrait survived the artist's momentary destructive doubts and can now be seen by future generations."
Aitchison was born in Kincardine-on-Forth in 1926, and studied at the Slade School of Fine Art. His work focused on trees, birds, dogs and figures depicted in rich, pastel colours.
He was elected to the Royal Academy of Arts in 1978 and awarded a CBE in 1999. Several retrospectives have been staged, including one at the Gallery of Modern Art in Glasgow in 1996.