Accidentally pushing a cork into a wine bottle is a common mistake. If you want to remove the cork and don't care about destroying it, you can dissolve it in a solution of nitric acid. Nitric acid breaks down natural cork over time and is commonly found in many cleaning products available to consumers.
Pour enough of a cleaning product containing nitric acid into your wine bottle to cover the cork. The cork will eventually stop floating and submerge in the acid.
Set the bottle, uncovered, outside or in a well-ventilated area -- away from pets and children.
Allow the nitric acid to dissolve the cork which may take several days, depending on the concentration of acid in your cleaning product.
Pour the out the nitric acid -- once the cork has dissolved -- and dispose of the solution as recommended by the guidelines in your cleaning product's Material Safety Data Sheet, or MSDS.