Open TTD – Configure Station Exclusively for Drop-Off or Loading

Assuming you don't want to break the station in to separate stations and use a load of feeder links, you will need to tweak the advanced option that limits your maximum station spread.

This advanced setting (specifically Stations→Max station spread) can be adjusted to values between 4 and 64, with a default of 12, and determines the maximum size square that can be allowed to bound each station (whether compound or not).

The recommendation is to only increase this if you are using the YAPF pathfinder, but this is the default so if you've never tweaked that setting there's no need to worry.

For more information, you can see the wiki entries for the setting and station spread.

If you need a station larger than 64 by 64, well then I think you're stuck (and possibly doing it wrong).

This station is exactly like a passenger station that both generates and accepts passengers:

• the wood that is being generated there needs to be taken to another station that accepts wood.
• the station will accept wood from other sources, but never from itself.

None of the cargo is "absorbed" by the local sawmill - you will need to transport all of it away, and if you want that local sawmill to generate goods you will need to transport wood in from another source.