This is a follow-up to Neutron Star mining. Assuming that problem can be solved, it would eventually degenerate to something similar to this case. And if it can't, white dwarfs seem like the next best source of stellar-mass quantities of elements heavier than helium. (And maybe thinking up solutions to this slightly easier problem will help illuminate potential solutions to the harder version.)
So, suppose you want to incrementally mine material from, and eventually completely disassemble, a white dwarf star. ("Incrementally" meaning "let's not just trigger a supernova and pick up the pieces afterward".)
What would be the easiest, most plausible means of accomplishing this using foreseeable technology? (I.e., something that does not require new physics, just potentially ludicrous amounts of time / resources, for which we can do back-of-the-envelope physical calculations.) It is permissible to assume any necessary conditions on the particular star's inherent characteristics or environment, such as that it must be part of a binary system or have pre-existing planets or somesuch, but fewer and weaker preconditions are of course better.