Hey there,
I have some steps that you can try:
1. Run the game under low graphics. You can change the settings if you can have The Sims 3 launched.
2. Delete all the cache files. Some files may be corrputed and deleting them will force the game re-create them. A link to tell you how to do that is here: https://help.ea.com/article/how-to-clear-your-cache-for-the-sims-3-on-a-mac
3. Try playing the game in windowed mode. In your Mac, /Users/<username>/Documents/Electronic Arts/The Sims 3/
Double-click the options.ini file to open it in Notepad (Win) or TextEdit (OSX), and locate the following line. Edit it according to the values stated below, then save the file and exit the text editor application.
fullscreen = 0
- Value "0" means windowed mode
- Value "1" means fullscreen mode
4. Do you have any mods or custom content installed? If yes, some may be out-of-date and may be conflicting with the game. Try deleting the mods or moving them out of your Mods folder to your desktop temporarily and then run the game. If your game runs properly, then there is definitely something wrong with the mods.
I hope any of these works.
Good luck and tell me if your issue is resolved or have any questions.