You might say:

Allez, du vent !

to keep the old fashioned aristocratic tone.

Some alternatives:

Ouste !

Du balai !

Dehors !

Hors de ma vue !

A plain rendering is "Allez-vous en !". If spoken it must be pronounced with force, unless the context is clearly one in which the hostility of the speaker is apparent. Given no special context, this can mean simply "Go away!", as when giving someone the advice to leave one place for their own good.

"Hors de ma vue !" conveys the displeasure of the speaker, which can be great if the phrase is pronounced with force. This is then a preferred form to render "Away with you!", as this latter communicates no friendly feelings, at least usually.

There is also the colloquial "Décampez !" (Décampe ! in the second person singular).

(TLFi) B.− P. ext., fam. [Le suj. désigne une pers. ou un animal]
2. S’en aller au plus vite, s’enfuir précipitamment.

This could still be used in a formal context as it is not labelled "popular" (populaire), as for instance "Foutez le camp !".

(TLFi) Pop., fam. Foutre, ficher le camp.

However, the verb "déguerpir" would be an option that is formal enough.

• Déguerpissez ! — Déguerpis !