Iggy, the sink drain can be removed from underneath. You will need a large adjustable wrench to loosen the nut that is located on the underside of the counter. Then disconnect the other end of the drain pipe at the trap. The pipe and attached drain lift out through the top of the sink. Be careful at this point, the drain pipe is the only thing that secures the glass sink to the counter.
I don't think a plunger would have worked to clean out the crud in the drain, as it would have just partially opened the blockage without really cleaning it all out.
2010 Georgetown 373
2013 Jeep Wrangler