Hi Isobel,
I think aspies definitely have a different way of grieving to NT's.
My dog died two years ago and then my grandad died last November and my cat died this march. I found I didn't respond the same way anyone else seemed to and it bothered me as I thought I must have something wrong with me or be a really bad person as the death that bothered me most was my dog.
The link mandapanda has put on is amazing and you should read it as it explained to me why I feel the way I do and you might find the same thing.
I found that I was pretty slow to start grieving and that when I did I didn't even realise it. I was fine at first but then a month or so later I started having really bad nightmares and my autistic traits (especially sensory problems) were really bad and I couldn't understand why. I only realised it was grief after other people told me and even then I didn't realise how much of what I'm struggling with is actually just part of an aspies grieving process until I read mandapandas link.
Try not to judge yourself by the way others grieve and just accept your way of grieving as as valid as anyone else's.