Like so many phrase
s in Japanese
(or any other language), the meaning of "shitsurei shimasu" is not
adequately explained by giving the "equivalent" English phrase for one of its applications. There exists no 1:1 mapping between words in different languages
In fact, "shitsurei shimasu" can mean the exact opposite of beable's "translation", as it is also used , e.g. when entering someone else's home.
For a broader explanation, let's first look at the literal meaning, which is quite enlightening: shitsurei means "impoliteness", and shimasu is the neutral polite form of the verb to do. A literal translation might be "I'm doing you an impoliteness" (since Japanese quite often depends on context to supply subject or even tense of a sentence).
Basically, the phrase is employed to preemptively seek excuse for small impolitenesses that hardly anyone would feel offended by anyway, such as leaving a meeting early, "invading" someone's home (even though invited), or (as an employee at a shop) briefly obstructing a customer's view of the merchandise while passing in front of them in a narrow alley between the shelves.