There's an Asteroid Mining Module (I think that's what it's called) that you can research. These go on ships, or on space stations.
What I did was equip my asteroid mining ships with 1 hull space of cargo, then some Asteroid mining modules. Then, as a fleet, they move from asteroid to asteroid, carrying 1 or 2 mass throwers. When they arrive they unload the mass throwers and start mining automatically. After a 5-day cycle I set up the mass throwers to throw minerals at one of my worlds. Then you forget about them until the asteroid runs out of minerals.
The problem I'm facing is that I have not yet figured out how to issue a mine order to a mining ship. I have a ship design with cargo and a mining module but when I go into the orders menu for its task force and look at the various orders I can issue it: mining doesn't seem to be one of them.
Here's my miner design:
Juliet class Asteroid Miner 17250 tons 283 Crew 485. 4 BP TCS 345 TH 62 EM 0
179 km/s Armour 1-59 Shields 0-0 Sensors 1/1/0/1 Damage Control 1 PPV 0
Maintenance Capacity 18 MSP
Cargo 5000
Asteroid Miner: 2 module(s) producing 20 tons per mineral per annum
Nuclear Thermal Engine E0. 8 (1) Power 62. 5 Fuel Use 8% Armour 0 Exp 1%
Fuel Capacity 50,000 Litres Range 65. 0 billion km (4200 days at full power)
Geological Survey Sensors (1) 1 Survey Points
This ship is classed as a commercial vessel for maintenance purposes
As for freighters vs mass drivers, I hadn't gotten around to playing with mass drivers and the idea slipped my mind to be perfectly honest. I may do that since there seems to be a glitch I'm having recur where an order such as "unload all minerals at Earth" keeps moving itself to the top of the queue no matter how many times I delete it unless I clear all the orders for the freighters. The mass drivers might be just the ticket since I'm looking for just that sort of "fire and forget" resource management solution.