Now back at the apparently impossible job of being a Palestinian cartoonist after his newspaper allowed him to return, he spoke for the first time about the challenges he faces to The Independent.
It was not the first cartoon he had drawn in his effort to show Islam in a favourable light. Another shows an open Koran as the filament within a light bulb, brightly illuminating its surroundings.
"My idea is that if you want to defend Islam against cartoons, you do it by drawing cartoons, not by killing the cartoonists," he said at his office in a university on the outskirts of Ramallah, the Palestinian political hub. "If you want to defend Islam against articles, write articles. If you want to defend it against ideas, than use ideas."
While Mr Sabaaneh agrees with the description of the Charlie Hebdo shootings as a terrorist attack, a major theme of his work since then is that such killings harm Moslems and Islam.
He said his drawing that sparked the controversy had been misinterpreted because he had not meant to depict Mohamed directly - but that if it was understood in that way he apologised. The man he drew, he insisted, was a follower of the Prophet spreading his message.
But that way of looking at it had not stopped the Palestinian president joining the fray. Just days after Mr Abbas joined the freedom of expression march with other world leaders in Paris, his office vowed "deterrent steps".
Mr Sabaaneh, 36, widely respected as a former prisoner of Israel and for giving voice to the Palestinian struggle, also had many defenders, however. His newspaper lifted his suspension after 10 days even though Mr Abbas's inquiry is yet to deliver its findings.
And although he exuded confidence, Mr Sabaaneh still has to be careful. He asked The Independent not to republish the cartoon, citing a directive from his own newspaper.
Offending religious sensibilities is just one of the hazards he faces. In 2013 he was imprisoned by the Israeli army for five months. According to his indictment by the Israeli military justice system, Mr Sabaaneh was guilty of "contact with a hostile organisation". He had published a powerful series on the plight of Palestinian prisoners, and is convinced he was incarcerated for his cartoons.
There is also censorship. Mr Sabaaneh has had many cartoons blocked by his editors, including ones about the Palestinian Authority, the PLO and an unflattering depiction of Egypt's President Abdel Fattah al-Sisi. He says that when he criticises Mr Abbas, he can only do so indirectly, without drawing him, and he fears his paper will now become more restrictive.
A cartoon he drew on the Isis executions of Egyptian Copts did not make it into Tuesday's paper. It showed a person about to be executed, but where his head should be, Mr Sabaaneh drew a mosque. He posts some drawings not used by his newspaper on a website, Cartoon Movement.
The polarisation between the rival Palestinian factions, Fatah and Hamas, is also a major problem, says Mr Sabaaneh. "The majority who are not related to Fatah or Hamas don't have their own media, so the balanced view is not reaching people," he said. "It won't find an outlet." He criticises Islamist movements for not accepting any form of criticism "because they believe they are sacred".
On his office wall is a huge poster of Naji Ali, the Palestinian cartoonist who drew against Arab regimes, Palestinian leaders and Israel - and was gunned down outside his offices in London in 1987. Mr Sabaaneh says Ali was a major inspiration, after he was shown his cartoons by his mother when just six years old.
He does not see eye to eye with freedom of expression absolutists, arguing that a cartoonist should not harm any religion. He was against the re-publication by Western newspapers of Charlie Hebdo's depictions of Mohammed. "Republishing them reactivates hatred and hostility. It's provoking more hatred in the society, based on religion."
Mr Sabaaneh's imprisonment did not lead him to tone down his drawings about Israel. One shows Jerusalem's Dome of the Rock mosque and a church being strangled by a huge viper with a Star of David on it. "Israelis have accused me of being anti-semitic," he said. "I see them, and not only their government, as not accepting criticism."
He says however that his main challenge is not from Israel, the PA or Hamas, but from his own audience. The controversial cartoon, he says, tried to challenge this. "I didn't mean to draw the Prophet Mohamed per se, but I left a vague area for the people to start questioning," he said. "This is our role, to provoke people to think. I want them to think about this issue."
- Independent