Your sentence is grammatically correct and easy to understand: Like a big delivery truck, blood drops off oxygen and food to the cells and picks up their trash.
To make it a bit simpler for a 6-year-old you could say:
Blood is like a big delivery truck: it brings oxygen and food to the cells and takes away their waste.
Why this works:
- The original sentence is fine. The comma after the introductory phrase helps the sentence read clearly.
- I changed "drops off" to "brings" and "picks up their trash" to "takes away their waste" because those words are a little simpler for young children to understand.