When you long press a photo in Snapchat you select Save to Camera Roll, video will probably be the same.
Then open Google's Photo app, switch to albums, and there should be one called Snapchat.
From memory, MIUI has no app drawer, everything is tossed onto the home screens ala iPhone. You just have to find the camera app since you can't delete it, being a system app.
If, however, the MIUI developers came to their senses and put apps in an app drawer like normal Android or you're using a launcher that has an app drawer, then look there.
Otherwise, install another camera app and use it instead.