The City of South Lake Tahoe's Building Division issues building permits for all construction activities and checks the work against the state building code and the City's own ordinances. Whether a particular cut needs one isn't something I'll guess at. If your job needs a City permit, we work out which office it goes through and help you file it before work starts, and when it's unclear, we ask the City.
Work in the City's right-of-way goes through a different office. The Public Works Engineering Division issues encroachment and obstruction permits for that work, and you'll find them on the City's permit applications page. If a pipe breaks under a slab while Development Services is closed, you can make the emergency repair, but you have to submit a permit application to the Building Division within the next working business day.
Most of the cutting we do around South Lake Tahoe is for homeowners, with some for property managers and small businesses. It's usually an older driveway or garage slab that needs a section opened for a drain, a line run through a foundation wall, or a damaged piece cut out so new concrete can go in.