What is the semantic relationship between the verbal phrases of a serial verb construction?
Is the temporal relationship the only one?


Most, but not all.

"我看水果"，"我切水果" and "我愉快地吃水果" are three separate SVO sentences. When we consolidate them into a single sentence, the temporal relationship between each verb phrase is there because these verb phrase must follow a logical timeline.


  我看(到)水果(就)切开它们(然后)愉快地吃 - Once I saw the fruit, I cut it and then happily ate it ,


I must see the fruit first, before I can cut it, and I must cut it first, before I can eat it.

Similarly:


  我大喝一聲, 我揮拳, 我打中他小腹 - I shout, I punch, I hit his lower abdomen
  
  我大喝一聲(便)揮拳打中他小腹 - I shouted and immediately punch and hit his lower abdomen


I shouted first, then I punch, and finally hit his abdomen 

However, not all multiple verb phrase has a temporal relationship like the examples above. They can happen concurrently.

Example:


  我吃飯，我看電視，我大聲笑 
  
  I have dinner, I watch TV., I laugh loudly
  
  我吃飯(的同時)(邊)看電視(邊)大聲笑
  
  I laugh loudly while I am watching TV. and having dinner. 


I have dinner, watch TV and laugh loudly at the same time.