I assume that this is either for a story or you're a supervillain looking to commit a very complicated crime. Either way, I support the idea.

If space travel is cheap and common, then it would be very difficult to stop other travellers from dropping by. Similarly, if Earth wanted to make a concerted effort to communicate with the colony, then Earth could probably communicate. So you've probably got to look at avoiding communication both ways.

First step: launch a vessel that can convert an asteroid to a low emissions stealth base. Obfuscate the launch with something like a false flight plan.

Second step: destroy all radio technology, delete all information relating to radio technology from the records. No radar, no radio, everything is hardwired.