The TWV (Tewerkstellingsvergunning) is a work authorization for people who do not need a visa, either because they already have one (regular short-stay visa like yourself, student visa…) or because they don't need one (people who don't need a visa for short stays in the Schengen area based on their citizenship, asylum seekers, Croatian citizens…), yet do not automatically have the right to work (unlike, say, other EU citizens who always have the right to work without needing either visa or a work authorization).
The TWV not a residence permit or long-stay visa, does not replace a visa and does not open any independent right to stay in the Netherlands. In fact, I don't know if that's what you did but what often happens is that an employer requests a TWV to be allowed to hire someone and that person then uses the TWV to apply for the right visa.
If you would have come to the Netherlands to work longer than three months, you would instead get something called a GVVA (Gecombineerde vergunning voor verblijf en arbeid or “combined permit for stay and work”), which is in fact a kind of residence permit and does also give you the right to stay in the country. But since you don't have one and merely have this work authorization, you are not allowed to stay after the end of your Schengen visa without another title (e.g. another visa, a residence permit or an extension of the visa you already have).