The correct form is 'Do you want to go and grab (or go to grab) some beer?' The construction 'go+ bare infinitive' and 'come+ bare infinitive' is very common in spoken and informal American English. Other examples are: 'Let's go eat' 'Come play baseball' You asked, 'Is it a common phrase that is not grammatically right?'. Well, it's certainly a common phrase. Is it grammatically wrong? No, it's not wrong. It's a simply a feature of the language, and it's the way that many native speakers speak. It's non-standard, but it's not incorrect.

From http://www.oxfordlearnersdictionaries.com/us/definition/english/go_1: In spoken English go can be used with and plus another verb to show purpose or to tell somebody what to do: I'll go and answer the door. Go and get me a drink! The 'and' is sometimes left out, especially in North American English: Go ask your mom!