Due to the strict visa control by the Saudi government, it may not always be possible to get a work visa. An indirect way, though, would be to get a business visa. However, your sponsor must convince the government that this visa is for a specific project and your stay would be only for a short duration (typically 2 months or so). The problem with this kind of visa is that it is suitable only for short-term working, for example, a turnaround or shutdown job in an industry. You will not be able to bring your family with this visa as you would have come to carry out a specific business in the kingdom for a short duration only.
Some people try to come on a visit visa, but if you are caught working for a sponsor and you have come on a visit visa, then you are asking for trouble, because this is illegal. Also, unlike the UAE, it is a herculean task to get a visit visa converted into a work visa.
In short, if you want to work in Saudi Arabia and you are looking for long-term employment, make sure that you have a valid work visa and the correct profession mentioned in your visa. This would save you from a lot of hassle later.