The Council shall by resolution order the City Manager to abate such nuisance or cause the same to be abated by having the weeds referred to destroyed by cutting, discing, or any other method in the discretion of the City Manager; his deputies, assistants, employees and contracting agents are hereby expressly authorized to enter upon private property for that purpose. Any property owner shall have the right to destroy or remove such weeds himself, or have the same destroyed or removed at his own expense; provided, that such weeds have been removed prior to the arrival of the City Manager or his authorized representatives to remove them.