When you assign any reference type—i.e. any object type—you assign a reference to the underlying object, you do not make a copy of said object. If you want to make a copy of the old array, then you need to do that explicitly during then assignment to the new array variable. There are several ways you may do that, here are examples of two.
Using SugarCube's built in clone() function:
<<set $newArray to clone($oldArray)>>
Note that clone() makes a deep copy of the object—i.e. if the array contains other objects, they will be cloned as well.
<<set $newArray to Array.from($oldArray)>>
Note that Array.from() makes a shallow copy of the array—i.e. only the original array is copied, any reference types contained within are left as references to their original objects.