I recently bought a sandwich from Subway. However while I was ordering a vegetarian sandwich I think the woman behind the counter never heard me and put something which looked like beef on my sandwich; I quickly told her to remove it as I didn't want meat. Did this make the sandwich haram? As I'm sure the meat was not halal and if yes, they how can I correct my mistake of eating it without knowing it has turned haram?
Well if you ate it without the meat everything should be fine inchaAllah:
If you ordered a sandwich without meat and when eating found out there is meat inside, and didn't continue eating the meat, also everything is fine inshaAllah as it was not your intention to eat meat and normally you will taste the meat easily and stop eating. So what you could and should do is of course to spit out any meat you have in your mouth. And repent and try to be sure that in future your order has been done and completed as you ordered it!
And remember that Allah says:
... And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful. 33:5
And Allah knows best!