Using a laser may seem cool, but any mining company is going to look at cost effectiveness, and give your laser idea a pass.
While heating materials to plasma temperatures is a pretty important step to running a "Santa Claus Machine", the energy needed should come from something cheap and simple to operate: a solar mirror. Since you are in free space, a mirror of any arbitrary size can be made and extended out of simple metal foil, and focused on a point on the asteroid to heat, vapourize and ionize the material to create the plasma stream.
Since the composition of the asteroid is likely to be a mixture of materials, and the ejection of a stream of gas or plasma is going to cause the asteroid to move, a few more steps need to be taken.
Firstly, the asteroid should be encased in a foil "pouch" to capture any out streaming gasses, water vapour etc. which are also valuable resources. The heating of the asteroid is likely to cause materials to escape through fissures in uncontrolled ways that you as a miner want to avoid. The solar energy can be sent into the asteroid through a transparent port in the pouch.
Secondly, the stream of gasses should be collected into a chamber to be heated to plasma temperatures by a secondary mirror. This allows for finer control of the process than erecting a continent sized mirror and doing it in one step.
Finally, the plasma can be streamed into the Santa Claus Machine to be separated through a mass spectrometer via magnetic fields, and the separate ions of purified materials (separated by atomic weight) collected in cold traps. If the company is simply interested in mining, the process ends there with purified materials being bundled together for shipping to industrial centres, otherwise the materials are used directly via 3D printers or other assembly devices to make products for use or for sale.
There will still be station keeping issues as jets of gas are collected from the asteroid, and manipulating the mirrors won't be "easy", but the essential simplicity of the scheme compared to the mass and complexity of a laser (and all its associated hardware, power generation, heat rejection apparatus etc.) will make it compelling to any profit minded company.