On private property, including your own driveway or a fenced job site, Mauldin requires no container permit. The City's solid waste chapter is written about its own residential service and does not reach a container on private ground.
The public way is a different matter and Mauldin publishes no route into it. There is no encroachment or obstruction permit for a container anywhere in the City's streets and sidewalks chapter, and what the chapter does contain is a prohibition: it is unlawful to place or allow to fall on any street, alley or sidewalk any material that is unsightly or that obstructs or tends to limit the use of the public way for its intended purpose. The solid waste chapter adds that no one may place garbage or refuse in a public street, alley or other public place. With no published permit, a street position has to be taken up with the City directly, and your account manager will do that for you.
Two City rules put the work on you rather than on us, and both are useful to know. Every contractor, carpenter or builder, or the property owner, must remove all trash arising from construction or alteration at their own expense, during the work as well as after it. And construction material is barred from City receptacles outright, with the code naming carpet, padding, sheetrock, lumber, shingles, siding, shutters, bricks, blocks, cement and mortar, concrete, rocks and dirt. There is no City route for any of that, which is precisely the gap a container fills.
Larger users are pushed the same way. A non-single-family user needing more than two City carts is not eligible for City pickup and must use containers, restaurants are not eligible at all, and for multifamily property the City says plainly that it does not collect and that the owner must engage a private provider.