I can say it happens to me when I play the game with pretty high settings.
Posting my important specs for the win:

Mobility Radeon HD4850 512MB GDDR5
Intel i7 960 Quad-core 2.80GHz
8GB DDR3 RAM

With these specs, when I run the game with:
  • Display Mode: Windowed
  • Window Size: 1920x1080
  • No AA
  • General Drawing Quality: 8 (Standard)
  • Background Drawing Quality: 5 (High)
  • Shadow Detail: Highest
  • Texture Quality: High
  • Texture Filtering: Standard
  • Ambient Occlusion: OFF
  • Depth of Field: OFF
the game runs pretty fine, no stutters or whatsoever (still some stuttering while walking in the bushes), but in two cases, which are:
  • Setting Window Size to 2560x1440
  • Setting Antialiasing to 4x MSAA
anytime when someone:
  • Teleports (Initiation and Finalization)
  • Use Food (the animation of the status Well Fed)
  • Pays for the Workshop support
the game will incredibly stutter going to 2-4FPS until the animations are done, then it goes back to normal.

It has to do something with graphic settings being high reaching a certain condition, but you guys know better than me on these things, so I'll leave it up to you =)

Also, I remember playing with a Windows XP system with an nVidia GeForce GTX250 512MB GDDR5 and things like the past stuttering with rain and the current stuttering with bushes, including the heavy stuttering quoted before, weren't able to experience. May be a Graphic Card support issue?