Can't find the experiment because of no keywords for it I can think of, but this shows that even a few 100 kilos have real amounts of gravity.
Edit: Here it is: http://en.wikipedia.org/wiki/Cavendish_experiment
"Evaporate some more nitrogen off that asteroid, Joe, we need to blow this dust away."
Really, you're not vacuuming up objects, they're just along for the ride in their immediate atmosphere.
(...And in space, you have no atmosphere to manipulate.)
EDIT: Looks like I was a bit late, I wrote this comment ~hour ago but didn't post it till now. :P
4/3 * pi * r^3
Using Ceres as a benchmark for typical asteroid density, an asteroid of radius r has mass
[volume in meters^3] * 2077 kg/(m^3)
On the asteroid's surface, acceleration due to gravity is
[Gravitational constant] * [mass in kilograms] / (r in meters)^2
which simplifies to
(6.67384E-11 * 4/3 * pi * 2077 * r) m s^-2
If we mine on a 1km diameter asteroid, the dust we kick up will accelerate towards the surface at 2.9 * 10^-4 m/s^2. A dust cloud 10 meters high will settle in about five minutes.