Can I change the order of clauses in the following sentence?

I don't think it's correct to change the order of the clauses in the following sentence when we are going to show the result of an action:

The bomb exploded, destroying the building.

But present participles can also be used to give the reason for an action:

Knowing she loved reading, Richard bought her a book.

Here I'm not sure if we can use the participle clause after the main clause:

Richard bought her a book, knowing she loved reading.

As you noted, participle phrases can be used for a number of reasons. Besides what you listed, they could also show simultaneous action:

Whistling joyfully, she skipped down the sidewalk.

Your concern is that one use implies cause-and-effect:

He fired, hitting the deer in the head and killing it instantly.

Swapping the order of phrases has little effect on the participle phrases that showed a reason for an action or simultaneous action ("She skipped down the sidewalk, whistling joyfully"). But it's understandable that you would hesitate to invert the cause-and-effect example, putting the effect before the cause:

Hitting the deer in the head and killing it instantly, he fired.

However, this is not so much a violation of a grammatical rule; it's simply cumbersome and difficult to understand. Yes, you could invert these sentences as well, you just might not want to.