If the neighbor's branches protrude onto your own property, it's often annoying. Find out here when you can and can't cut off the branches.
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Better to talk to the neighbor
If these branches and twigs bother you, you may cut them off at the border. Affecting doesn't mean you don't like them. Then you mustn't. However, if this is interfering with the growth of your own plants, if the branches are hanging on your terrace and are struggling for your space, or if you want to set up a climbing frame for the children and the branches are in the way, then cutting off the branches is permissible without further ado. But before that you should probably talk to your neighbors - so that you don't get into trouble.