On private ground, a driveway, a yard, or a fenced job site, Mount Vernon does not make you pull a permit for the container itself. Keep it on your own property and you are clear.
The street is a different matter. Mount Vernon's street rules say that anyone who places a container, a stand, building material, or any other object on, beside, or over a street or sidewalk in a way that blocks the free flow of traffic has to get a permit first. The code names a container in those words, so there is no grey area about whether it applies.
There is also a second route for building work. The city council's street committee can grant a special permit to occupy a street with building material during construction or repair, on the condition that it takes up no more space than it needs and the work moves along quickly.
Applications run through the City's online permit portal, which the City lists on its applications and forms page. The permit desk takes questions at 360-336-6214. The City does not publish a fee or a review time for this one, so build in a few extra days. If you are not sure where your property line stops and the right-of-way starts, your account manager can point you to the right office before you commit to a delivery date.
One city rule matters more than the permit. Mount Vernon runs trash and container service as a city utility, and its rules make use of that city system compulsory for every property. The city's definition of solid waste includes construction and demolition waste, and the city rents out its own roll-off containers for that work. Your Prime Dumpster account manager checks how the rule applies to your address before anything is scheduled.
Before you book, confirm with the city that a container can be placed for your job at your address. Rules differ from city to city and they change. Your Prime Dumpster account manager will help you check, and will tell you plainly what your options are here.