If I have a landscape contract at an apartment building and one of the tenants keep doing my job which costs me money, i there anything that I can do about it?

You can enforce the terms of your contract against the landlord--that's all you can do. If the landlord agreed to pay you, for example, $400 per week for landscaping, the landlord must pay your $400 per week for as long as the contract is in effect (but see below), whether or not the builidng needs it or whether or not someone else has done your job for you. You have the rights, and are entitled to the money or compensation, the contract gives you.
Note that a contract that doesn't guaranty certain work or pay for a defined or set period of time (e.g. a 6-month contract, a 1-year contract, etc.) is one that can be suspended or cancelled at will. If the contract does not guaranty you the work or pay for a certain period of time (or a certain number of visits to the property), then the landlord would be free to not have you do the work, and therefore not pay you. This also means that if you just an oral (often incorrectly called "verbal") agreement with the landlord, since such are not enforceable for a fix duration (only written contracts may be), the landord could again have you not do the work if it has already been done.
You have no rights against the tenant, since you and he/she are not contracted and you have no authority over him/her. The landlord could force the tenant to stop if the landlord wanted to--the tenant has no right to do anything to the landord's outdoor space--but is not required to do so.