There are several types of PhD students in Switzerland, among them are:
University/laboratory employees. These receive a monthly salary of about 3 to 4.5 kCHF (the exchange rate is approximately 1 to 1 with the US$, there are rare variations above and below this range) and have to pay a tuition that is typically in the range of 500 to 1200 CHF per year. This salary is low in comparison to the standard of the country (the median salary is about 7000) but enough to comfortably cover the cost of living and some extras. To get on these positions, you apply to them like a regular job and in an increasing number of cases, you have to apply to a graduate school. These contracts frequently include teaching duties, TA work, sometimes infrastructure work (like lab maintenance and management). Having a part-time job besides these position is not necessary, but not unheard of. Note that depending on the location, if you are issued a full time contract, you might legally not work for another employer.
SNSF-funded doctoral students. (rare in the experimental sciences, more frequent in the humanities). These applied to a grant, with the collaboration of a professor or senior researcher. They receive a stipend typically lower than the above category but still in the order of 3000 CHF. They don't have teaching duties. For part time jobs, see above.
Industry-funded PhDs. Companies like large pharmaceutical companies offer industry-based PhD studies in collaboration with the local university. I've heard mixed feedback on these, since they are often paid like a PhD student but require industry-standard commitment and constrains. No chance of having another job in general.
'Freelance' doctoral students typically ex-members of the two first categories who ran out of time as a regular student and didn't manage to finish their thesis during the time they where funded. These people have another job and try to finish on weekends and evenings. Allow 10 years until graduation.
With all this being said, I have a hard time understanding your situation, PhD studies in Switzerland are rarely funded with a 'scholarship'. I think you need to figure it out with the institution you are interested in first. It's rare that PhD students have another job, some do a bit of consulting, some have a start-up, but the PhD is typically a full time job.