A lot of space debris on LEO are small 1 to 2 cm pieces. Removing these threats is a concern to anyone using LEO. Can a cube/micro satellite use collected small debris and propel them to both deorbit the debris and gain orbital velocity itself? A small rail gun perhaps.
In theory, yes. But in reality, no - not yet, and probably not ever.
If you could build an ideal collector, something to sweep debris into an inlet where it could then be accelerated to raise the satellite's orbit, then this could work. But in reality, to try and catch debris with a different vector to the satellite's (and possibly dramatically different velocity) would require manoeuvres, and these would consume a large amount of propellant, and probably require a very large collector, whether it be a net, a magnetic funnel of some kind...which also requires more impulse to move etc.