Mulligans
General Mulligans
In general, you want to get your Coldlight Oracles early. Any high cost cards should be pitched, with the exception of Skulking Geist versus Evolve Shaman; whether you are first or second, a Skulking Geist in your starting hand means that you can ruin their game plan on turn 5 as second player (hold your Coin for this), or on turn 6 as first player. Don't play the Oracles without a way to bounce them - they are highly targeted.
Other good cards in the start of the game are Doomsayers, Tar Creepers, Backstabs, and Youthful Brewmaster (which I've played without bouncing anything just to put a body down).
Aggro Mulligans
Against Aggro I tend to want cards to slow them down. Sap is an interesting choice, but some decks use buffs to get minions ramped up early. Bouncing an early play of a big minion can be very handy as well (double Enervate+Coin? Bounce that!). Vanish isn't a mulligan pick generally, but I'm not upset if I get one early enough to bounce a whole horde of buffed minions from a token druid.
To be fair, I expect to lose most matches against Aggro. I've beaten a pirate warrior, but it wan't via fatigue - I used my creatures and spells to eliminate his minions, and managed to get a few copies of Prince Valanar going (Valeera the Hollow to duplicate them, them bouncing them and duplicating more). Druid token is a little easier, since they rely more on buffs - bouncing creatures eliminates buffs, and the Skulking Geist can even catch Mark of the Lotus or Earthen Scales.
Control Mulligans
Control Priest is a good matchup. They often don't play much until later, and if they manage to use Barnes to get a target for their Eternal Servitude you can Sap it to their hand, and now they are forced to hold it until turn 9 or 10. Y'Shaarj isn't even that scary, since he's milling their deck for you. If you can hold him off for a turn, then Vanish the army of of play, you've eliminated a big chunk of his power.
Handlock is likewise doing your job for you, and they have one way to come back later in the game - their Death Knight calling all their demons back. Fortunately, you have 2 Vanishes as well as the board clearing Wild Pyromancer/Plague Scientist to clear big waves of minions.
Jade Druid is the hardest of the lot, but is doable. Try to take the smaller minions out without needing your big removals, and at the end you need to stall him out while milling.
I’ve always liked fatigue/mill decks, and with the rise of a lot of late game decks I wanted to play mill rogue again. The loss of Gang Up hurt mill rogue badly, but Valeera the Hollow can help make up for it a bit, and a few new tricks round the deck out. This deck is based on Senfglas’ KFT Valeera the Hollow Mill Rogue (http://www.hearthstonetopdecks.com/decks/senfglas-kft-valeera-hollow-mill-rogue/).
The substitutions to Senfglas’ list so far are:
-2 Gadgetzan Ferryman; +1 Shadowcaster, +1 Plague Scientist
-1 Youthful Brewmaster; +1 Wild Pyromancer
This results in a little less ability to bounce cards but the Shadowcaster generates a 1 cost minion, which can be handy, and acts like a Shadowstep when used on a Coldlight Oracle, generating a 1-cost Coldlight. Plague Scientist with Wild Pyromancer gives a board clear, or the Wild Pyromancer alone can be used to clear smaller minions against certain decks (Shaman, Token Druid, Hunter). The fact that the Shadowcaster makes a duplicate rather than bouncing can be exploited by then Vanishing the board, getting you 2 copies of the Shadowcaster’s target.
Jade Druid (especially the Miracle variant) were always a sore spot for Mill Rogue, but the new Skulking Geist helps combat their ability to resist your fatigue. Sure, they may still get a few cards advantage, but if they don’t recognise the threat they’ll likely draw some cards with Wild Growth or Nourish , helping you mill them. A big Ultimate Infestation to fill their hand is especially fun, if you follow it by pitching a bunch of their favourite cards with some card draw. Skulking Geist also works well to take the fangs out of Evolve Shaman as well.
The environment currently doesn’t have much aggro in it (Token Druid, Pirate Warrior are about the most aggressive), making it a relatively good environment to play with Mill decks. Edit: Thanks to aggro decks being less common for me the last few days I am up to 50% win rate with it.
Edit 2: post jade druid nerd the deck is doing better, am at rank 9 now.
A recent match; I misplayed by not doubling up my Doomsayers at the end, but it demonstrates why the Jade Druid’s card draw is an advantage for Mill: https://hsreplay.net/replay/gQPzPxxQckGX5HDSKDfj2d