It's unfortunate, but Kartana simply doesn't have the strong, physical movepool that it is screaming out for. Its only good STAB moves are Smart Strike (70 base power, doesn't check accuracy) and Leaf Blade (90 base power, 100 accuracy). These moves are naturally staple on Kartana in my eyes because of a) STAB, and b) decent base power. Reliable coverage options to include are Sacred Sword and Night Slash, but with Aegislash recently banned, i'm seeing a lot more merit in running Swords Dance over Night Slash to compliment its ridiculously high base attack of 181. Steelium-Z is also a great option for Kartana, Giving it a very powerful STAB option, which would even be a difficult to take move by mons that resist steel.
When it comes to bulk, Kartana is pretty meh. 59 hp is obviously not good, but coupled with grass / steel typing as well as 131 defense means that Kartana can take a wide array of physical hits quite well; but with that being said, Kartana prefers not to have its hp whittled down, as a life orb set alone already makes it somewhat of a glass cannon. On the special side, Kartana is as strong as wet paper, with 31 spd and 59 spa, Kartana can't do anything at all regarding special stats.
For me, one of Kartana's most crippling factors is the base 109 speed. It's such an awkward speed tier to be competing in. Just short of the base 110's and reaching a speed of 348 with jolly, Kartana can't quite keep up. Beast boost doesn't prove useful to this problem either, as no matter what the situation when building, Kartana's attack should always be higher than its speed, unless you run a timid nature with 19 attack IVs. Choice scarf is a very meh option, as Kartana can't pivot properly without access to u-turn (which it doesn't learn) as well as the fact that Kartana as a revenge killer and late game sweeper is not best utilizing it's role, being a physical wallbreaker from my experiences.
Although not a bad pokemon, Kartana will struggle to an extent in holding its own weight once the meta is settled down; I look forward to see what people can do with this mon ^-^