Quite a few problems with your code:
On Arrays.asList returning a fixed-size list
From the API:
Arrays.asList: Returns a fixed-size list backed by the specified array.
You can’t add to it; you can’t remove from it. You can’t structurally modify the List.
Fix
Create a LinkedList, which supports faster remove.
List<String> list = new LinkedList<String>(Arrays.asList(split));
On split taking regex
From the API:
String.split(String regex): Splits this string around matches of the given regular expression.
| is a regex metacharacter; if you want to split on a literal |, you must escape it to \|, which as a Java string literal is "\\|".
Fix:
template.split("\\|")
On better algorithm
Instead of calling remove one at a time with random indices, it’s better to generate enough random numbers in the range, and then traversing the List once with a listIterator(), calling remove() at appropriate indices. There are questions on stackoverflow on how to generate random but distinct numbers in a given range.
With this, your algorithm would be O(N).