There is a dead dog shown in the climax of Se7en.
Is there any significance to this image?
...but there are a couple of possibilities..both involving Mill's dogs.
The Mills' have dogs in their home...
Firstly, it's possibly as a reference to another draft of the script in which it wasn't Tracy's head in the box but the head of one of Mill's dogs..
...according to Brad Pitt, at one point the studio seriously considered putting the head of Mills’s dog in the box, rather than Mills’s wife.
...“With Se7en, I said, ‘I will do it on one condition – the head stays in the box. Put in the contract that the head stays in the box.’”, the actor told Entertainment Weekly in 2011.
Secondly, possibly as a foreshadowing of what is to come.
Mills refers to his dogs as "the kids"...by showing a dead dog it foreshadows the death of Tracey and her unborn child.
Finally, it's just possibly there for comic effect so that John Doe can say..
"I didn't do that!"