There are two things to do in your case:
1) Remove the object from the array
2) Delete the object itself (only if you want to, sometimes the array is just a temporary storage)
In the case of nodes, that's how you do it:
var node = array[0] # Get the node at 0
array.remove(0) # Remove from the array
node.queue_free() # Delete the node
Note that removing from the array will shift all following elements by one place, for example if there is an object at index 5 it will now be at index 4.