How can I delete character from a string by compare with another string

OriginalGriff beat me too it, but posting mine anyhow, since it solves a couple of other issues. It preserves ascending order and deals with the trailing comma you have in one of your strings.

using System;
using System.Collections.Generic;
using System.Linq;

namespace DemoApp
{
	public class Program
	{
		public static void Main(string[] args)
		{
			string string1 = "1,2,3,4";
			string string2 = "2,3,5,9,10,";

			// Convert strings to integer arrays to facilitate later sorting
			int[] set1 = GetIntegers(string1);
			int[] set2 = GetIntegers(string2);

			// Get all of the numbers that appear in either set1 or set2
			IEnumerable<int> union = set1.Union(set2);

			// Get all of the numbers that appear in both set1 and set2
			IEnumerable<int> intersection = set1.Intersect(set2);

			// Get the list of numbers we want (union minus intersection) in ascending order
			IEnumerable<int> unionExceptIntersection = union
				.Except(intersection)
				.OrderBy(value => value);

			// Join the numbers back into a string
			string result = string.Join(',', unionExceptIntersection);

			Console.WriteLine(result);
		}

		private static int[] GetIntegers(string text) => text
			// Split values around commas
			.Split(',')
			// Convert string values to integer values (or null)
			.Select(strValue => int.TryParse(strValue, out int intValue) ? intValue : (int?)null)
			// Eliminate invalid integer values
			.Where(value => value.HasValue)
			// Convert to non-nullable integer value
			.Select(value => value.Value)
			// Convert the sequence to an array (so we can iterate more than once)
			.ToArray();
	}
}

0) Split the strings on comma delimiters.

1) Add each array's element (from the Split statement) to a HashSet object (a HashSet will not allow duplicate element values).

2) Output the contents of the HashSet object.

string[] parts1 = string1.Split(',', false);
string[] parts2 = string2.Split(',', false);

HashSet<string> hash = new HashSet<string>();

foreach(string part in parts1)
{
    hash.Add(part);
}

foreach(string part in parts2)
{
    hash.Add(part);
}

foreach(string part in hash)
{
    Console.WriteLine(part);
}
Console.ReadKey();

The benefit of using a HashSet object is that it will not throw an exception if you try to add a duplicate value. Instead, it simply won't add it. A HashSet is not guaranteed to be in any order, so I leave it as an exercise for the programmer to return the values in the desired sequence.