This is an interesting questiion. What exactly do they modify? The answer is, of course, if they modify a noun, you need to use the adjective, and if a verb, then the adverb. Now, the first sentence, while common, isn't really correct. [Edit: Fumblefingers' comment makes me think twice about that. Anyway...] Look at these:
If we must kill them, let us do so quickly and cleanly, without excuses.
If we must kill them, let the killing be quick and clean, without excuses.
In your first sentence, these two constructions are getting crossed: it actually refers to the killing. However, it is also more concise than us do so. There are times when informal conversation performs this sort of abbreviation at the expense of absolutely correct grammar. In this case, of course, the most concise version is:
If we must kill them, let it be quick and clean, without excuses.
Clearly, the it refers to the killing. Perhaps the reason that the sentence sticks with the adverb is because the noun killing hasn't been mentioned, so there's a bit of an added thought process to mentally fill it in.
This tendency to abbreviate is probably why you will often see this substitution of an adjective for an adverb, especially in AmE:
If we must kill them, let us kill them quick and clean.
You pretty much have to learn on a case-by-case basis when colloquial English will allow this sort of transgression and when it will not.