Hi LandsHeer,
I see you edited your post to indicate you have tried the support depths, but did you watch the video tutorials on Nvidias site for Destruction with PhysXLabs? Tutorials Here
I’ve not tried making a SpeedTree asset as destructible before, but ultimately it’s a static mesh so all should be possible. There are some caveats to using PhysXLabs and destructibles with meshes that have certain features though.
- if you’re mesh has holes or uncapped sides PhysXLabs will not cap those for you. You will need a complete mesh.
- using single planes (ie. the leaves) can cause issues when the mesh is fractured causing spikes.
These two things along with some really helpful information about destructibles can be found by opening the PhsyXLabs > Help > PhsyXLab Help button. This will bring up a helpful documentation for using it along with images for demonstration an dhow to fix these issues.
The best place to start with this is by watching the video tutorials linked above. The ones that refer specifically to support depth and giving you an example are “Jersey Barrier with minimal overhead” and the “Multiple FBX” one. With the last one you may not be using multiple FBXs but support depth is key. A lot of the videos go over support depth and setting it up but these are the two that may help you more. I would recommend watching them all though and to do the tutorial for practice to help you get more familiar with PhysXLabs and destructibles.
As for the collision issue…how are you setting up collision? Is this something that is handled with the SpeedTree asset or is this something you’re setting up custom? If you’re using the Mesh editor/viewer and adding collision here you may want to avoid the auto-generate as this will cover you’re entire mesh. You would want to use simple collision boxes and scale them to the necessary size or use an external program to make you’re own custom collision.
I hope this has helped and if you have any questions feel free to ask! 
Tim