/mnt/something has root as Owner. So When I try to move something to Trash, it’s not allowing me to do
You have to change permissions or owner of that folder (not /mnt itself but the subfolder “something”).
If I’m not wrong changing permissions is enough to use gui “move to trash”, you can use chmod thru cli (man chmod) o your gui file manager with root privileges.
If you want only your user be able to read/write to that disk, then change the owner using chown thru cli (man chown) or again your gui file manager.