It's even easier than that. Instead of sliding the notification off the screen, slide it ever so slightly to the right. It displays this little gear thing, and you can block all notifications for that app from right there. I have a stock Nexus phone so YMMV.

It's roughly the same in iOS. I have almost every app notification disabled. I'll just check them when I check them, rather than getting distracted.

For me, it's under:

Settings -> Sound & notification -> Manage app notifications

This took me several minutes to figure out because I had a mental blind spot to "Sound & notifications" due to the fact that the option has a speaker/volume icon. I made the mistake of trusting the icon as a sincere shortcut for understanding the text it's supposed to represent.

This is just what I was looking for, surprised I didn't find it already. Thanks.