The incident, a punishment for voting, occurred in western Herat province, police spokesman Raoud Ahamdi said.
The Taliban had warned people not to participate in Saturday's vote.
The two candidates are former Foreign Minister Abdullah Abdullah and former Finance Minister Ashraf Ghani Ahmadzai.
They have both pledged to improve ties with the West and sign a delayed security pact allowing nearly 10,000 US troops to remain in the country for a further two years.
Voting in Saturday's poll was described as relatively peaceful despite a series of Taliban attacks that officials said had killed more than 50 people.
The dead included five election workers killed when their minibus was destroyed by a roadside bomb in Samangan province.
Vote counting has begun and official preliminary results are due to be announced on 2 July, with the final results coming on 22 July.
Officials are also looking at dozens of electoral fraud complaints.
The United Nations Assistance Mission to Afghanistan condemned the mutilations in Herat.
"Like millions of their countrymen and women, these ordinary Afghans were exercising their fundamental right to determine the future path of their country through voting and not through violence and intimidation," said Jan Kubis, UN special representative.
"By their vote, they already defeated those who promote terror and violence."
The Independent Election Commission said initial estimates suggested that more than seven million Afghans voted on Saturday, about 60% of the country's 12 million eligible voters.