Mr Raut said Mr Gandhi was among those who had made appeals to the government to save Memon.
"Gandhi had used all his powers to save Yakub Memon. He even had written to the President. I want to ask (opposition) what kind of mindset is this," he told reporters.
Responding to the Shiv Sena's charge, Congress leader Anand Sharma said, "On what basis are they questioning him? Gopalkrishna Gandhi is a 'Gandhian'. He has always been against any form of violence on human beings. In that context if he's opposed to death penalty then his views should not be distorted and given a communal colour."
"Congress doesn't need certificate from Shiv Sena when it comes to sacrificing in the fight against terrorism," he added.
In July 2015, Mr Gandhi had written to President Pranab Mukherjee to "reconsider" the rejection of Memon's mercy plea.
Opposition parties' vice presidential candidate Gopalkrishna Gandhi has said he will file his nomination tomorrow.
(With inputs from IANS)