The "Instant" card type and the "Flash" keyword are removed. If a card has the "Flash" supertype, they can be played at any time you have priority. (Like a card with the flash keyword).
In official formats, if you mulligan down to 6 or fewer cards in hand you may scry 1 at the start of the game. In TumbledMTG, instead each player gets to scry X, where X is seven minus the number of cards in their hand. This means the more you mulligan, the more you scry.
Each player may mulligan once 'for free', remaining at seven cards.
The 'legendary' supertype present in official formats is removed. It has been replaced with a 'Unique' supertype. Players may only include one copy of any given unique card in their deck. (Players can still include multiple different unique cards in their deck. Players cannot have a copy of a given unique card in both their library and their sideboard.) (Consider this and this when deckbuilding.)
Players may have up to 20 cards in their sideboard, rather than 15.
Player one and player two each begin the game with a different emblem, pictured to the right.
The last step of a library being searched is for it to be shuffled by its owner. 'Shuffle your library' is left off of cards that search your library in TumbledMTG, and it's simply assumed it must always be done by the library's owner.
Like official formats, players roll dice (or otherwise use chance) to decide who goes first. If the player who wins the die roll draws their hand before choosing whether to go first or second, they are forced to choose going first. This isn't a new rule, but it's more relevant to this format.
If a nonsorcery (ie, creature, enchantment or artifact) spell is copied, the copy will behave much like you would expect a normal spell of that kind to behave. When it resolves it will be put onto the battlefield as a token permanent.
If an ability can only be activated at 'nonflash speed', that means it can only be activated any time you could cast a nonflash spell.