What is the Sharia ruling on an accountant's refusal to sign off on unjust deductions by order of his manager, and would his leaving the job at that point be considered cutting off his livelihood?

It is not permissible to cooperate with a sponsor who oppresses his workers. If you know that the deductions are unjust, cutting from the worker's wage without right, then it is not permissible for you to implement the deduction. You must refrain from carrying out the order, advise the sponsor, and clarify the truth to him. If your refusal leads to leaving the job, then know that whoever gives up something for the sake of Allah, Allah will compensate him with something better.