The First Minister said failure to do so would mean the anti-independence group led by former Labour Chancellor Alistair Darling would not be "living up to their rhetoric about a clean campaign".
His intervention came as a pro-independence website defied multinational company Vitol and re-posted its initial article from 12 days ago which it had been forced to take down under threat of legal action.
Lawyer for the group Aamer Anwar has written to Vitol's lawyers accusing them of "an outrageous attempt to bully the National Collective into silence" and vowing to "fight any legal action and test every allegation in the courts".
Mr Taylor was unveiled by Better Together as its biggest donor but Vitol, the company of which he is president and chief executive, has been involved in a series of controversies.
These range from paying $1 million to a Serbian warlord later unmasked as a war criminal, to being forced by a US court to pay $17.5 million over its dealings with the Saddam regime in Iraq.
British and overseas news organisations have reported on Vitol's controversial operations involving Iran, Congo, Libya and the UK itself, where it was reported to be in negotiation with Her Majesty's Customs and Revenue over the past use of Employee Benefit Trusts.
As a major donor to the Conservative Party one Labour backbencher criticised this as "dirty money", but Mr Darling has defended both Mr Taylor and his donation.
Mr Salmond said: "The problem for the No campaign, and Labour in particular, is they cannot on the one hand criticise donations from this source – as they have done – and use the other hand to grasp the money now offered to them from the same donor.
"There are a variety of serious and legitimate concerns which have been raised about this donation. In these circumstances, the only reasonable course of action for the No campaign is to return this donation immediately – and that is exactly what they now need to do if they are intent on living up to their own rhetoric about a clean campaign."
The National Collective describes itself as "an open and non-party political group of artists and writers campaigning for a better Scotland". Its website carried a piece about Mr Taylor and Vitol which attracted legal threats that forced it to take down the site last week.
Ross Colquhoun, director of the group, said: "Such corporate bully-boy tactics are an attack on freedom of speech. We will not be silenced or bullied by legal intimidation. This is the world's largest oil trading company but it will fail if it tries to intimidate us. This is Dave versus Goliath and Goliath will not win."
The author of the article, 21-year-old Glasgow University student Michael Gray, said: "I have never been a member of a political party. This is about the freedom of every Scot, from whatever political background, to ask the tough questions of politicians and their funders at a crucial time. We don't have the money or the resources Vitol has, but we have principle, and that is priceless."
He joked that his parents had said he may have "a granny bond in the attic worth a few hundred quid" but he had no funds stashed away offshore.
A spokeswoman for the company responded: "Vitol is pleased the National Collective has chosen to incorporate some of its comments in the revised article. However, factual inaccuracies remain."
Speaking ahead of Labour leader Ed Miliband's speech to Labour conference in Inverness today, SNP Westminster leader Angus Robertson said: "Attempts to silence critics of the No campaign have backfired spectacularly, and Mr Miliband should use the opportunity of his visit to Scotland to answer the questions about this scandal."