I'm trying to get this pipe out but I have no idea how to remove it from the sink. Any ideas?
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Pliers and screwdriver are a poor substitute for the proper tool. ( They may or may not work but are not easy to use and may result in bending or damaging the thin metal of the drain basket without getting it to turn )
The proper tool is a Drain Removal Wrench
It has two ends, one small one large, with nubs that fit into the slots of the drain. It has flat sides so you can get a large adjustable wrench ( crescent wrench ) on it or It has holes in the handle so you can put a screwdriver through them to act as a lever for turning leverage.
You need a way to keep the pipe and basket underneath form turning and since you do not have a tradition basket with nut you will need a strap wrench or adjustable pliers ( channel locks ) to hold the pipe assembly. It will probably take 2 people, On to hold the assemble under the sink while the other try to turn the drain wrench counterclockwise.
Based on the photo it has some corrosion and If this does not work you may have to cut it off from below with reciprocating saw ( saws-all )