use AppleScript version "2.4" — Yosemite (10.10) or later
use framework "Foundation"
use scripting additions

set aFile to "/Users/me/Documents/1/2/3"

set aNum to 1
set bFile to getUpperDir(aFile, aNum) of me

–> "/Users/me/Documents/1/2"

set aNum to 2
set cFile to getUpperDir(aFile, aNum) of me
–>"/Users/me/Documents/1"

set aNum to 3
set dFile to getUpperDir(aFile, aNum) of me
–> "/Users/me/Documents"

–与えられたパスから指定階層「上」のパスを求める
on getUpperDir(aPOSIXpath as string, aNum as integer)
　　if aNum < 1 then return aPOSIXpath
　　set pathString to current application’s NSString’s stringWithString:aPOSIXpath
　　repeat aNum times
　　　　set pathString to pathString’s stringByDeletingLastPathComponent()
　　end repeat
　　return pathString as string
end getUpperDir

use AppleScript version "2.4" — Yosemite (10.10) or later
use framework "Foundation"
use scripting additions

set aPOSIXpath to "/Users/me/Documents/" –AppleScriptのPOSIX path表現（フォルダを表現するさい、末尾に「/」）
set catDirList to {"1", "2", "3"}
set bPath to getChildPathByAppendingDirsByArray(aPOSIXpath, catDirList) of me
–> /Users/me/Documents/1/2/3

set aPOSIXpath to "/Users/me/Documents" –CocoaのPOSIX path表現（フォルダを表現する場合でも、末尾に「/」入らず）
set catDirList to {"3", "2", "1"}
set cPath to getChildPathByAppendingDirsByArray(aPOSIXpath, catDirList) of me
–> "/Users/me/Documents/3/2/1"