Rubble fell down the 30m-high (100ft) cliff in East Cliff on 24 April and partially engulfed the Edwardian funicular carriages.
Bournemouth Borough Council said the carriages had been removed but work to stabilise the slope was continuing.
Environment boss Larry Austin said "all options" were being looked at for reinstating the lift.
He said: "We remain committed to the future of a cliff lift. However, it will be some time before these assessments are made and any necessary stabilisation work commences. The cliff lift will not reopen this summer.
"Our next step after the removal of the final debris is a thorough assessment of the site to consider the next course of action."
An abseiling team was used to secure the carriages of the East Cliff Lift to the running rails ahead of their removal.
A temporary road closure remains in place along East Overcliff Drive while the work is carried out.
A cliff railway which was damaged by a landslide in Bournemouth will not reopen this summer, a council has said.