So, I use an Italian version of Rpg Maker Vx Ace which come with italian-translated scripts.

Since the battle system utilize the Vocab script to print lines in battle, it's possible to replace the non english Vocab script with the english version?

Clearly I'll just copy-paste the original script without edit.

Have you tried modifying the TERMS, within the DATABASE section of TOOLS?

Yes but unfortunately those terms refers only to words.

I can translate the words: "Magic", "Attack", "Defend" etc... in the database but the sentences are stored in the Vocab script. 

There are the sentences like: "An enemy approach",  "In which file do you want to save?" "X Obtained the victory" etc.. that are now in my native language :/

if you have it on steam, you can change the language by: tasto destro sul mouse, proprietà e vai su lingua, e dovvrebbe riscaricarti il programma in inglese

Nice, thank you.

I guess doing that changes the database as well as the scripts. I have many projects that I would prefer to keep in my language so the best solution for me would be to replace the vocab script just for this project so that I can deliver it entirely in English. Clearly if this is not possible I will do as you advised me and proceed with reinstalling the tool.

I will allow this exception to the rule.  You may use a script/plugin that converts Italian to English.