Replay Hearthstone games?

Unfortunatetly there is no way to watch your previous game in the Hearthstone client, neither on mobile nor on PC. And if you are on mobile, there is no way of doing that at all as far as I know, besides recording your games as some kind of video and rewatching it (which I actually did on PC in the very early days).

However, there are some 3rd party tools that you can use for this purpose. Hearthstone Deck Tracker is one of the most popular ones. Besides it's tracking and stattistic features, it also allows you to rewatch your tracked games, which is exactly what you want.
If you are concerned about bans for using 3rd party software: Ben Brode (Lead Designer of Hearthstone) confirmed that using such a tool is fine:

any app that duplicates what you can you do with pencil and paper already is fine

Source

Even though some player still have concerns since the tool directly accesses the game's memory, I never heard of anyone getting banned for using tools like this. And with the big userbase it has, it is fairly unlikely that it is ever going to happen.

There is no built-in way to replay your games in Hearthstone at the moment. You can anyway use third party programs to parse your game log and create a "virtual replay".

The new beta version of Hearthstone Deck Tracker for example, in addition to the normal overlay functionalities it has, uploads a replay of the match to HSReplay to be viewed at a later moment.