The "spacer" is a mack washer turned upside down. Its nothing special about the "spacer" itself. Whats different is the exposed overflow and the mack gasket...what HJ is calling the spacer between the lavatory and the overflow assembly. Thats not typical. Usually the overflow is integral to the bowl and no extra mack gasket is needed in that space. It would be factory made into one assembly.
I'm not saying go wild and tear it all out. By all means if it stays in tact and in in good shape you cna leave that "spacer" alone.
Loosen the large nut until it stops at the bottom of the threads. if it will not turn the use a saw and carefully saw it on two sides and pry it off. It will fall into two pieces.
Now cut the lower mack gasket into with a razor knife and carefully remove it. The entire drain will now lift up and there will be a gap between the lavatory and the chromed brass flange that you see when looking down into the lavatory.
While holding the bottom "half" of the pop up assembly...grab the rim of the flange inside the lavatory with some channelocks and turn the flange counter-clockwise to unscrew it. It will come apart and the rest of the pop up assembly will drop out of the bottom. The p-trap should also be removed by now.
If the upper mack gasket is rotten you can get another at any good plumbing repair specialty store or a good hardware store thats local owned.
I like Delta or wolverine brass all chromed brass pop up assemblies. There is also an American standard brass pop up I like. Kohler makes a fine one. Dont buy a plastic one and do not buy a cheap knock off thats chromed brass made in china......they are garbage and the stoppers do not have enough travel. Grohe also makes a nice pop up.