Relative can live here in Saudi

That will be a major major problem.

Only direct dependents are eligible for sponsorship i.e. children and spouses.  Even parents are not generally approved for permanent residency i.e. Iqamas. 

The only way to be able to sponsor your grand daughter is through proper documentation.  You must legally adopt her and / or show documentation that gives you full legal custody for her.  These documents need to be translated into English/Arabic and attested by the Saudi Embassy in your home country.  They may even ask for more documents e.g. NOC from mother or death certificate attested in case she passed away etc etc.

The rest is then up to your employer and how effective their PROs are.  But it is not a straightforward process.