The threat was directed at Bapi Dutta, a Congress leader of Birbhum district.
"Bapi Dutta, it would not take me even a minute to behead you," shouted Monirul Islam, Trinamool's member of assembly from Labhpur in Birbhum district, at an election rally.
Continuing in the same vein, the Trinamool Congress MLA claimed he had "squashed" three people under his feet for committing atrocities against women.
Dutta, the target of the verbal attack, reacted sharply: "There is no doubt that Trinamool Congress is a party of anti-socials. People will give Islam's comments a befitting reply through the ballot."
The threat comes close on the heels of the party's Birbhum district president Anubrata Mandal saying at a rally: "If Independent candidates issue threats, set fire to their houses."
Asking the people not to vote for Independent candidates, many of whom are believed to be dissident Trinamool workers, Mr Mandal said: "If the administration thinks of supporting the Independents, then hurl bombs at the police and the administration: I am telling you."
However, facing widespread criticism, Mr Mandal backtracked on Thursday claiming it was a "slip of tongue".
The State Election Commission (SEC) has asked the state government and the district administration to take steps against Mr Mandal, but nothing has been done so far.
The opposition parties asked the SEC to take action after Mr Islam's comments were aired by local television channels.
CPI-M state secretariat member Rabin Deb said the "despicable" comments by Trinamool leaders like Mr Islam were vitiating the atmosphere and encouraging anti-social elements.
State Bharatiya Janata Party president Rahul Sinha said the SEC's failure to take action has triggered a wave of such comments by Trinamool leaders.
"Had the commission taken action in previous such cases, these leaders would not have dared to make such comments," he said.