Just use ${@:2}. It is explained here perfectly.
And to pass it into another script:
./anotherScript "${@:2}"
Of course it will not pass it as array (because you cannot pass an array), but it will pass all elements of that array as individual parameters.
Okay, lets try it this way. Here is your first script:
#!/bin/bash
echo "Here is my awesome first argument: $1"
var=$1 # I can assign it into a variable if I want to!
echo 'Okay, and here are my other parameters!'
for curArg in "${@:2}"; do
echo "Some arg: $curArg"
done
myArr=("${@:2}") # I can assign it into a variable as well!
echo 'Now lets pass them into another script!'
./anotherScript 'Wheeee' "${@:2}"
And here is your another script:
#!/bin/bash
echo 'Alright! Here we can retrieve some arguments!'
echo "Here we go: $@" # that is including 'Wheeee' from the previous script. But we can use the same trick from above if we want to.