The Remove method of ComboBox can be used to delete an item.
private void DeleteButton_Click(object sender, RoutedEventArgs e)
{
foreach (var item in ComboBox1.Items)
{
if (((ComboBoxItem)item).Content.ToString() == FindTextBox.Text)
{
ComboBox1.Items.Remove(((ComboBoxItem)item).Content.ToString());
return;
}
}
}