I decided to make a Sawk set from scratch (that is, without looking at the on-site sets and analysis, or the somewhat out-of-date move list) to see what it could do against the most common hazards leads. Apologies if there's already a set posted here that's too similar.
Anti-Lead Sawk
Sawk@Fighting Gem
Choice Band
Nature: Adamant
EVs: 4 Def / 252 Atk / 252 Spe
Ability: Mold Breaker
-Close Combat
-Taunt
-Ice Punch
-Stone Edge/Earthquake
Close Combat is the primary cannon, Taunt stops hazards, Ice Punch stops other hazards, and Stone Edge stops some hazards and otherwise provides good neutral coverage. It has low accuracy though, so don't bet the farm on it. Earthquake does better neutral coverage and stops cockblocking by Weezing and other poison types but does less against hazard setters. Taunt won't really stop walls from walling Sawk, since you have to switch out afterwards, but it can help out an allied wallbreaker. (I'm personally a fan of sending in Lum SD Samurott on any Alomomola that stick around...)
Stealth Rock
Armaldo - Close Combat right through frailer variants. If you think it's a bulky supporter, Taunt it.
Bastiodon - Close Combat right through all variants.
Carracosta - Close Combat through all variants.
Golem - Close Combat to the moon.
Golurk - Ice Punch if you're feeling lucky about their EVs and your damage roll, otherwise Taunt will work.
Lairon - Close Combat gets the job done. Earthquake will not quite get there against max defense Lairon.
Metang - Earthquake is the move of choice here for damage, but if you want to avoid rocks, Taunt it.
Piloswine - Close Combat right on through.
Probopass - Either Close Combat or Earthquake will work.
Regirock - If you're feeling very lucky, you can Close Combat. Otherwise Taunt will stop the rock.
Seismitoad - Close Combat will work against offensive or specially defensive sets. Otherwise you will have to Taunt.
Torkoal - Torkoal is bulky as fuck, so Earthquake if you want a 2HKO. Taunt if you hate rocks.
Spikes
Cacturne - Ice Punch and Close Combat will both evaporate the cactus. Unless it's max defense, in which case you want CC. Taunt works either way.
Garbodor - Earthquake will 2HKO, but Taunt will be needed to avoid hazards.
Glalie - It's actually too fast to taunt without a Jolly nature, but you might miss out on some otherwise narrow KOs. If you go Adamant, this is one of only two hazards setter on this list that will do its job. Close Combat works too if you go Jolly.
Maractus - Close Combat is the best, but Ice Punch works against 252/0 variants. Taunt works too outside of sun.
Roselia - This is why we pack Ice Punch. It will work against 252/0 specially defensive Roselia. Otherwise you need Taunt.
Scolipede - It's going to get something up. KO back with Stone Edge if you have it, otherwise Taunt is the only way to stop the second layer. The only hazard setter on the list that can stop Sawk's stopping all the time.
Toxic Spikes
Garbodor - Earthquake will 2HKO, but Taunt will be needed to avoid hazards.
Roselia - Again, this is why we pack Ice Punch. It will work against 252/0 specially defensive Roselia. Otherwise you need Taunt.
Scolipede - It's going to get something up. KO back with Stone Edge if you have it, otherwise Taunt is the only way to stop the second layer. The only hazard setter on the list that can stop Sawk's stopping all the time.
I probably missed a hazard setter or two, but I'm pretty confident Sawk can beat the rest. (I guess you need stone edge for Ariados, so keep that in mind?)
EDIT: Went with DTC's suggestion to use Fighting Gem over Band. It misses out on insta-gibbing Roselia, but you can still taunt it and Roselia won't be doing much back. 2HKO with Ice Punch if it stays in.