Before getting on to the alternatives, the repetition of cloth in the original sentence is odd. The only reason I can imagine for it being worded like that is if you were watching a demonstration and the person speaking paused between the mention of the cloth and the explanation that it was a damp cloth.
In a written form, this would be expected:
Now I’m going to wipe the work surface with this damp cloth, to remove all the crumbs and scraps of food.
Note that I don’t think the comma is necessary after ‘now’. Again, I presume that in the original, the speaker paused before explaining the next stage.
From your list of alternatives, these are possible:
Now with/using this damp cloth, I am going to wipe all the crumbs and scraps from the working surface.
Now I am going to wipe all the crumbs and scraps off the working surface with/using this damp cloth.
Now I am going to wipe off all the crumbs and scraps from the working surface with this damp cloth.
Now I am going to wipe all the crumbs and scraps off of the working surface with this damp cloth. <-- US use. ‘Off of’ is not yet standard in the UK, thank goodness.