In my mind, there can be at least two different problem:
1-Your tileset is not 32 pixel
2-Your tilest has an offset which is different of the tile size
In this case you need to post-processing your tileset.
It looks like you’re either trying to cut this up into larger tiles than it actually has, or the artwork is offset in the file. There’s no overlap in the image you showed, rather, the tiles cuts are made in the wrong place. it also looks like the tile-set might be pre-zoomed, so you’re not cutting it at the right size (your “32px” cuts contain 16x16 visible pixels).
Could you please show the original tileset (the source file, not a screenshot from Tiled), it would help figure out what exactly went wrong. If you can’t show the whole thing, then a portion of it that includes the top left corner would be enough.
The tiles at the top could be either 16px or 32px, the rock assets are on a 16px grid, and the tiles at the bottom seem to be on a 16px grid, so I’m guessing this is a 16px tileset, not 32px as you’ve been trying to use it.
That seems to have done the trick! Thank you! If I may ask another question: I had been hoping to use this tileset along with a couple others on my map (not on the same layer, of course), but the other tilesets definitely are 32x32. My background layers are composed from 32x32 sets and my map is set to 32x32, and when I try to use the rock tileset on a new tile layer on the map, the 16x16 tiles are too small. Is there any way to fix this so I can use the sets together, or can I not mix 32x32 sets with 16x16 sets, even if they’re on separate layers?
Short answer: No, you cannot mix tile sizes within a single map.
Long answer: There are two possibilities, but both come with their own hassles.
If you set your map to 16x16 tiles, you can use the 32x32 tiles as “metatiles” consisting of 2x2 blocks of 16x16 tiles. This will effectively lock you out of many convenient tools, such as the terrain tool, so it might not be practical. If you’re placing all your tiles by hand anyway though, it might be worth trying.
You could edit the rock tileset to be 32x32. You could either scale the existing tileset up and hand-edit it to not be pixelated, or rearrange the existing tiles and fill in the resulting gaps (for example, the horizontal/vertical edge tiles would get absorbed into corner tiles, so you’ll need to make new ones).
Personally, I’d ditch this tileset and draw/find another one that’s designed for 32x32, you’ll probably waste less time that way.
@AltruisticBad9 Did you consider contacting the author to ask about how this tileset is meant to be used, or maybe to ask for help with adjusting the tileset to your needs? Where did you get this tileset?
Showing the problem you’re having can also help the author to avoid such problems in the future, or if this tileset works fine in another map editor as-is, then maybe we can improve Tiled such that it would also be able to work better with this tileset as-is.
It seems to have been an issue of conflicting tile sizes! My map is 32x32 and the tileset seems to be made for 16x16 maps. Just as a test, I created a new 16x16 map in Tiled just now and created a new tileset for it using this same sheet, and it worked just fine!
If there’s a way to make it so Tiled can use 16x16 tilesets with 32x32 or vice versa, that’d be fantastic, LOL. I just started using Tiled this month though, so I have no idea whether or not that’s plausible, haha.
Well, if you’d like to use those graphics anyway but need to combine it with other tiles that are 32x32, then I’d suggest making a scratch map with 16x16 tiles and that 16x16 tileset and then painting 2x2 blocks on it that you’d like to use as tiles on your 32x32 map. You can then export this map to an image and use that image as a 32x32 tileset in the actual map.