There are many synonyms for the phrase "drinking up" that describe the action of finishing a drink. These include "hoisting," "swilling," "knocking back," "chugging," "slugging," "gulping down," and "quaffing." Each of these words has a slightly different nuance or tone, and some are more informal or slang than others. For example, "chugging" or "slugging" might suggest a more aggressive or hurried drinking style, while "quaffing" has a slightly old-fashioned feel. No matter which synonym you choose, the message is clear: you finished your drink quickly and efficiently.