It comes after a Spanish Supreme Court judge last week dropped international arrest warrants for Catalan separatist leaders.
The 61-year-old St Andrews University academic was arrested in March by police in Scotland following a European Arrest Warrant issued by Spain on charges of violent rebellion and misappropriation of public funds for her role in the unconstitutional independence referendum in 2017.
A four-week extradition hearing was due to begin in Edinburgh next week.
But a Spanish Supreme Court judge on Thursday dropped European and international arrest warrants for deposed Catalan regional president Carles Puigdemont and five other separatist leaders, including Ponsati, who fled abroad.
The decision came after a German court ruled that Puigdemont could not be extradited to Spain for rebellion, only for embezzlement connected to the alleged misuse of public funds.
Ponsati's warrant was formally discharged during a short hearing on Monday at Edinburgh Sheriff Court, but she remains in exile as she is likely to be arrested if she returns to Spain.
Spanish arrest warrants remain open, meaning those who were fighting extradition could be detained if they returned to Spanish territory.
Speaking outside the court, former education minister Ponsati said: "I am just determined to keep fighting for the freedom of all political prisoners, for civil rights in Catalonia and Spain and for the Republic of Catalonia."
In a statement, her lawyer Aamer Anwar said: "This is a humiliating defeat for the Spanish state which since October 1 has unleashed a wave of repression, attacking the Catalan people, suspending their government, jailing or trying to jail independence leaders.
"The withdrawal of the warrants is a tremendous victory, but there can be no mood for celebration whilst nine Catalans are held as political hostages and Clara remains a political exile unable to return home for at least 20 years."