Broadwater Cemetery has run out of space for new burials and will be closed soon.
Linda Thorne, whose sister is buried there, said she found its current condition "really upsetting and heartbreaking".
Worthing Borough Council said it had been given approval to maintain the cemetery as a "wildlife haven".
Ms Thorne said graves and monuments were being broken up by weeds and trees because the area was not being looked after.
Her wheelchair-bound mother had also been unable to visit her daughter's grave in recent years because of the state of the paths, she said.
Ian Hart, a funeral director, said he thought the state of the graveyard was disrespectful.
Tom Wye, of the Friends of Broadwater Cemetery, said: "Making a cemetery into a nature reserve is not a licence to do nothing."
He said he sympathised with the council as funding had been cut over the last four years but the site still needed to be actively managed.
Worthing Borough Council said the site was now considered a nature reserve because of a lack of space for new graves.
A spokesman insisted the cemetery was still being looked after with the grass being cut four times a year.
However, grass cutting was now "less intensive" with a focus on "meadow management" in places where there is wildflower interest, he said.
Relatives of people buried in a Worthing cemetery have criticised how the local authority maintains the site.