I am unfamiliar with this word. Looking through Google image search it seems to mostly refer to larger bags, often with a drawstring, or somewhat larger, more rugged handheld bags, and usually they are less “nice” and often less permanent? Contrast with a “Tasche” which are usually fancier and more permanent and may be smaller, including but not limited to what we would call a “purse”, or a “Tüte” which is more like a disposable shopping bag?
A purse would be Geldbeutel or Portmonee/Portemonnaie, a Tüte is almost never a Beutel. Beutel are something permanent (made from thick plastic or, more common, from fabric) and, if without further specification, they are usually large enough to fit more than one item.
At least that is how I would differentiate between these words, as a South-Western German. People in the east or north will probably use these words differently.