The breacher saw says it can cut through any door in the game. This includes keycard doors (but sadly not lever activated doors). This opens up 5 solo levels to some time saving routes (2.3, 2.9, 4.8, 6.9, and 7.7) and potentially several more for online co-op. Here is the list of everything I've found and at least theorized on.

1.11 CLEANUP At the end. May save time in multiplayer by being able to do slow-mo room last.

1.12 MEET BIG BOSS Online co-op: May save 2-3 seconds not having to walk to the keycard as long as one of the players is still using sniper support for the guy on the front balcony. Although the player grabbing the keycard death warping to catch up to the other is likely faster.

2.1 MEETING BART Online co-op: one player can clear the right half of the level without having to wait for keycard. Death warp to top player for slow-mo room.

2.3 GOING UNDER Solo: Go down to kill everything. Ignore keycard and go back up. Online co-op: one player waits at the top, skipping the climb back up.

2.7 OUTPOST Online co-op: One player goes up the left side of the building to clear the window areas so first player can snipe the far right street level guys. By the time they're done there should be enough bar again to saw into the keycard room.

2.9 THE BLOCK Clear everything to the top but don't pick up the keycard in the slow-mo room. Drop off to the right and finish level using saw, completely skipping building respawns.

2.10 CAUGHT IN A MAZE Online co-op: One player can saw through door and do top while other player does bottom. May require death warp and saving enough kills to get sniper support to clear slow-mo rooms.

3.3 METRO MADNESS [MAY NOT WORK] Online co-op: One player goes top, other goes down. Player that went down goes right, saws through door, and grabs keycard in dark room. Player that went top should arrive around this time. Do slow-mo room. Exit out different doors (unconfirmed if this will work). Player that went left reaches other slow-mo door last. Player that went right death warps to them to finish level.

3.8 HIPSTER BEER FACTORY Has a keycard door. Not practical for single player because of too much backtracking. Online co-op will probably get keycard before the other player gets to the door.

4.1 BANK HEIST Online co-op: Gets someone to the basement sooner, allowing team to cover more ground by splitting up. If bar permits, allows doing the final keycard room before the lowest basement level.

4.3 FIBONACCI [MAY NOT WORK] Online co-op: team can split up after first slow-mo room and save time not collecting keycard. Team enters upper and lower door to finish slow-mo rooms (may not work). Otherwise player that went up death warps to do lower slow-mo door and complete level normally.

4.8 WHINE AND DINE Cut the door ASAP to skip the entire backtrack through the level. DO NOT PICKUP THE KEYCARD! Grabbing it causes back spawns.

4.9 LIGHTS OUT Can't get enough bar for the first 2 doors. Doesn't save any time compared to grabbing the keycard from slow-mo room (which you have to enter). Huge time save for a donut run to cut down the door by the powerswitch, however!

5.3 DUSTY NEIGHBOURS Online co-op: second player can get through the door sooner then waiting for keycard to be collected.

5.11 WORD ON THE STREET Likely won't save time because of having to go to the keycard to get a gunner kill. In co-op one player would probably reach the keycard before the other could finish sawing the door anyway. Assuming they arrived there at the same time, which seems unlikely.

6.2 SNITCHES GALORE Online co-op: One player to go back up the ladder after the first slow-mo room and saw through to take a different route sooner. Activate the saw ASAP so other player can build up for sniper support.

6.3 GRAVEYARD SURPRISE Requires 2 uses of saw to get into locked basement without a keycard. Seems impractical compared to just getting the keycard solo or co-op.

6.8 POOL PARTY CRASHERS Online co-op: May save time over waiting for the keycard depending on the route.

6.9 DOWNSTAIRS CAGE Solo: Faster clear and easier approach on arrest target. Online co-op: Allows the team to split up and clear the basement sooner.

7.6 EARTHWORM BEN Online co-op: May allow second player to get to basement sooner.

7.7 SWITCH AND DESTROY Saves time for 3-star and leveled on first 2 keycards, and additional time for leveled on 3rd.

7.8 HOME BOX OFFICE Online co-op: Won't have enough bar for first door, but allows access to 3rd building sooner.

7.10 UNDER PRESSURE Online co-op: second player can get into basement sooner.

Let us know if you find any other things the saw can cut through!