#!/bin/bash


vars=(
  "/foo/bar/baz/qux/file.txt"
  "/a/b/c/d/e/f.txt"
  "/1/2/3/4/5/6/7.txt"
)

lefttrim=3

# remove root and first element
((lefttrim += 2))

xargs -n1 <<<"${vars[*]}" | 
    printf "/%s\n" $(cut -d'/' -f"${lefttrim}"-)