The construction "being beaten up" expresses the result,not the actual action of the beating (the verb "to be" being used in the present continuous
The sentence is not idiomatic, I don't know if it is even wrong.
I certainly can't think of a German version...

One would probably be more likely to say: "Having been beaten up", in German: "Da er verprügelt worden war, ...". Present perfect because it happened in the past but has consequences on the present.

Hope this helps.

having been beaten up,

I'm fairly sure that "Having been beaten up, ..." is grammatically correct, but I'm equally sure that nobody would say or write that, as it sounds slightly formal/pompous/old-fashioned (a bit of all 3?).

Somehow it brings back memories of Latin translations:

Bridges (having been) burned, Caesar proceeded towards Rome

... or something along those lines!

Bob: I wouldn't say it either (I cannot think of a situation where it would come up) - I only answered the question

Could you clarify what you mean by "passive participle constructions"? I don't believe I've heard of the passive participle.

It should be pointed out that the introductory phrase "Being beaten up" is not an example of use of the passive voice.

Grammatically, it is not the same thing as "He was beaten up by the thugs" or "He had been beaten up by the thieves," which are indeed examples of use of the passive voice.

The example describes Peter's condition after the beating: "He was (in a state of being) beaten up," hence, it is not an instance of the passive; rather, "beaten up" is in aposition to Peter (Peter, being black and blue; Peter, being in pain; Peter, being the worse for wear, informed the police).

English is ambiguous this way.

By the way, in my opinion, "Being beaten up, Peter informed the police" is perfectly grammatical and idiomatic. It may not be graceful, elegant, or a good stylistic choice, but it is otherwise unexceptionable.

Technically 'being beaten up, Peter informed the police' is grammatically correct, but, take another example 'Being beaten up, Peter tried to protect himself'. This is more clearly
correct. The problem is that in your example, you use the present participle. so Peter is actually in the process of being beaten up, and if the police are there he surely has no need to inform them. That is why 'Having been beaten up' is suggested,not for grammatical reasons.
The rule is briefly that the participle links to the noun to which it refers.
'Walking down the street, the trees came into Peter's view.'Clearly the trees weren't walking, it was Peter. The sentence is incorrect and would read better as 'Walking down the street, Peter saw the tree come into view.

Well, it looks like there's a bit of a disagreement. Bob C says "perfectly gramatical and idiomatic", cuwak says "not idiomatic", JGMcI says gramatically correct but doesn't venture an opinion on whether or not it's idiomatic.

I side with cuwak and Karen. "Being beaten up, Robert informed the police" is not idiomatic (not in my idiom, anyway.) Like cuwak and Karen, I would say, "having been beaten up..."

And I disagree with JGMcI further. (Sorry!) I don't find "Being beaten up, Robert tried to protect himself" is correct either. I think most would say, "while being beatem up, ..."

Martin(CA) I agree, but in my comment I was trying to stick to the original where the participle was used without the 'while' or 'as he'. Better examples
As he had lost his bike/having lost his bike, Peter had to walk to work.
As he had just sold his car/having just sold his car, Peter had plenty of cash in his bank account.
I'll pass on the idiomatic bit.

When I say that "Being beaten up, Peter informed the police" is idiomatic, all I have in mind is the frequent use in English of "being" to initiate a sentence or clause. Here are some examples to illustrate:

1597 Shakes. 2 Hen. IV, ii. i. 199 You loyter heere too long, being you are to take Souldiers vp.

1641 Milton Ch. Discip. ii. Wks. (1851) 61 Being they are Church-men, we may rather suspect, etc.

1815 Scott Guy M. ix, With whom he himself had no delight in associating, ‘being that he was addicted unto profane and scurrilous jests.’