The incident occurred in Odisha state on Thursday, police said.
Maya Murmu was at a tube well drawing water in Mayurbhanj district’s Raipal village when the wild elephant appeared out of nowhere.
Authorities said it had strayed from the Dalma wildlife sanctuary, nearly 200km from Mayurbhanj.
After being trampled, Ms Murmu was taken to hospital where she died from her injuries, police officer Lopamudra Nayak was quoted as saying to the Press Trust of India news agency.
Reports said when family members gathered for the funeral and were in the middle of performing last rites, the same elephant appeared, lifted Ms Murmu’s body from the funeral pyre and trampled it again, as shocked mourners looked on.
The family were only able to go ahead with the ceremony after the elephant left. It remains unclear if the animal harmed anyone else present.
Conflicts between elephants and humans are a common occurence in Odisha. Intensive industrial activity in the mineral-rich state has increased human encroachment in animal habitats, increasing chances of encounters between villagers and elephants.
A worrying trend in the state has also been a spike in the number of unnatural deaths of elephants. At least 1,356 elephants have died in Odisha since 2000-01, according to data provided by the state’s chief wildlife warden, reported the IANS news agency.
At least 42 elephant deaths were recorded in the state in just seven months from April to October last year.
Many other incidents of human-elephant conflict have been reported from other parts of the country.
In March this year, a woman was killed in an attack by a wild elephant at a forest in central Chhattisgarh state’s Bilaspur district. Her eight-year-old grandson was injured while trying to run away, police said.
In May, a 40-year-old woman was trampled to death by an elephant outside her house near Gudalur, in southern Tamil Nadu state’s Nilgiris district.