To add on to FumbleFingers' excellent answer.
The full context of the phrase is:
His broad face had lines of weariness in it, and he stirred his drink slowly with a glass rod, watching the cubes of ice slur clumsily about.
The three bold phrases reinforce the idea the character is tired, and possibly not thinking clearly, or perhaps that he is the less intelligent of the two characters in the dialogue. These little details (like Lupov's thinning hair) are not vital to the overall story, but they do help humanize the characters so the reader can immediately connect with them.
More than that -- the weariness, the slow stirring, the ice cubes slowly moving, the thinning hair, the occasional drinking, the eyes closing, etc. -- all are subtle examples of entropy, which is the main point of the story.
In this context the use of slur makes sense. You slur your words as you get tired (or, as FumbleFingers pointed out, drunk). In a similar way the objects in the universe will start to move more slowly as the overall level of energy runs down. Naturally, Asimov was well aware of this when he wrote these metaphors into the story.
On a related note: Even though slur is more commonly used with words and not physical objects, as you read English literature you should recognize that, as in any language, words can have both literal and figurative meaning. For example, suppose I write:
As he drank, his words listed from side to side like a schooner in a wild gale.
The dictionary offers several definitions for list as a verb. Given the context, the most relevant is: (of a ship) lean over to one side. Obviously words aren't ships and can't literally lean in any direction -- but as a figurative image, it should make a kind of sense.