Is it possible to get another Z visa without existing China to do the process back in my country

Yes, it's possible. You should quit the job of your previous employer peacefully and get a release letter. Then ask the new employer to prepare your work permit as soon as possible. Then go to the local exit and entry administration to renew your work permit and residence permit.

( direct quote from this website)
If you want to study at a different educational institution or work for another employer, it is permitted to do this without having to start from the absolute beginning and get a new visa. The first criterion is that you must do this while the existing Temporary Residency Permit is valid. The new organisation must be eligible in the normal way and must obtain all the new paperwork. There can be difficulties if the old organisation will not co-operate or positively objects as they might when you want to leave a job before the end of the contract. Realistically, a lot depends on the new organisation as it will have to lead and manage the situation.