Can Someone knows his/her business be interpreted as Somone knows his/her stuff?
Yes and No. It can be interpreted, but the interpretation is contextual. If it is not an idiomatic expression, it means what the individual words express. Therefore, it can mean anything defined under Business.
[5.] You can use business to refer to a particular area of work or activity in which the aim is to make a profit.
This is a broad definition. It can mean most generally e.g. the computer business, or more narrowly something out of the context, e.g. the business with restructuring the HR department. If profits are involved by definition, then "the business" may be the finance business, the free market, etc. This explains the more specific defintion:
[2.] Business is used when talking about how many products or services a company is able to sell. If business is good, a lot of products or services are being sold and if business is bad, few of them are being sold.
This can be expressed by "stuff" but it has lost most of this meaning. Stuff is only said in colloquial registers to mean quite the opposite: a thing in general, or indefinite quantities--that sort of stuff. However, compare for analogy German Stoff "textile", "fuel", "mater", "material", "substance" as well as the "theme" of a literary tradition, i.e. the stuff of legends. If the latter is from a sense of scripture ~ writing, then you might say Anne knows her books.
Compare for analogy: That's none of your business. (meaning: you have no part in this, it is not your concern). It would be unidiomatic to say "* none of your stuff" in most cases.
The opposite case is possible. If somebody rummages through your belongings, you might as well hear none of your business / not your stuff to strike a moderately friendly tone in an informal register, because both words have undergone semantic bleaching to a certain extent.
These are also in the dictionary
[8. ...] If she doesn't want the police involved, that's her business.
It's not our business.
[9. ...] You can use business to refer in a general way to an event, situation, or activity.
See there for synonyms and more. Watch whether each sense is singular, uncountable, or countably plural.
PS: "business" can also be a euphemistic slangword (cp. junk). It really really depends on the context.