Yes, you can do this just like a bottle of sparkling wine. It should keep the beer for a couple of days, but not forever. Sometimes the corks don't work great, so I would buy a Champagne bottle stopper like the one below Don't get the one that hold onto the ridge under the bottle opening.
If you're wondering how to store beer after opening, your best bet is to reseal it with an airtight cap or stopper to reduce oxidization and cease carbonation loss.
Do not use a vacu-vin, you will pull out carbonation and flatten your beer, also possibly oxidizing it. Also it will NOT seal, it's not like wine. You an use levered stoppers which put a little bit of give, but even those will pop out because of the pressure building up in the bottle when it's resealed.
Yes, a wine saver is an effective tool for preserving wine. The mechanism of the rubber stopper and pump works in sync to get rid of any possible air that slides into your wine bottle. Since it prevents your wine from oxidizing, you will still enjoy the same quality - taste and smell wise, even after several days.