The 30ft (9m) female at Felixstowe was one of three whales reported to have died on the East Anglian coast in recent days.
The operation took four hours and the waste will be taken to an abattoir for disposal.
A remaining cordon on a small section of the beach is due to be removed on Friday.
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Suffolk Coastal District Council said because of how decomposed the whale's body has become it was disposed of in large bins.
It was then transported to an abattoir in Melton.
It is hoped the high tide will wash away anything that remains.
Council spokeswoman Fiona McConnachie said: "Situations like this don't happen very often. When they do, it's a very sad event."
She added: "We'd like to apologise for any inconvenience and would like thank the public for their cooperation throughout the process."
The carcass of a dead fin whale which washed up on the Suffolk coast four days ago has been removed.