Parks spokeswoman Connie Chan said more than 200 trees have been damaged since September, with the most recent vandalism occurring last month.
The vandals have been targeting trees in sections of the park undergoing reforestation and are marked as so, Chan said.
She said the young trees, which are about 3 to 5 years old, cost about $250 each. The damage has cost the department about $50,000 in a nine-month period.
Chan said that cost does not include staff time and effort to grow and nurture the vegetation.
She said about 1,000 trees are planted in the park each year and, in an average year, about 20 to 30 trees are vandalized.
Chan called the situation "very disheartening" and said the vandals are taking advantage of signage marking the young trees and alerting the public to be mindful.
She said the trees are left to die and have to be removed after the vandals damage the treetops, which exposes them to disease and rot.
Park patrol units have been alerted to the situation and are working with the San Francisco Police Department to keep an eye out for more park vandalism.
The attacks on the trees that occurred in September and October and then again in May were mostly on the west end of the park, Chan said.
The San Francisco Forest Alliance, a group unaffiliated with the parks department, has pledged $1,000 for information leading to the arrest of the tree vandals.
The organization is calling on other environmental groups to match the award offer.
The group said they plan to work with police to distribute the money if anyone is caught in connection with the tree destruction.