Hi Behnaz,
bstone81 is correct about it taking a long time for Google to re-index so many 301ed URLs - has the issue improved at all in the last week?
If you search for snippets of content from your blog posts, are the new URLs on tcclinic.com showing up, or is the content still indexed under the old Shopify URLs? I've run a couple of these and I see them indexed in the two locations. Please see the following screenshot: http://i.imgur.com/fvawU9L.png.
The Shopify URLs return 404s (http://tcc-e-store.myshopify.com/blogs/news/11632829-luxe-diamond-foundation) - it's not guaranteed how long Google will take to re-crawl these pages and acknowledge that they are gone. Unfortunately, you can't 301 redirect them to speed up the process.
Unfortunately, some of these pages do NOT return a 404, even though your content is gone. See this example (the redirect plugin is from my former agency, and shows the headers the page returns and if there are any redirects):
Indexed content: http://i.imgur.com/QHSAnlR.png
Shopify's page, returning a 200 OK response but no content: http://i.imgur.com/TT9ZehC.png
Several post pages do return a proper 404 though: http://i.imgur.com/L30npnv.png
As Google says here, the best way to remove content is for the URL to return a 404 or 410 server response: https://support.google.com/webmasters/answer/64033?hl=en
That page also says that outdated pages not returning 404s will drop out if people stop linking to them. Try to change any and all old links that might point to the Shopify blog to your new URLs.
You also have issues with multiple versions of your content being indexed on many URLs within your main domain: http://i.imgur.com/Z7Hzz37.png
For this, you're going to want to look at pagination options. This post from my former colleague at Ayima is a really good one on this subject: http://www.ayima.com/seo-knowledge/conquering-pagination-guide.html. It was highly recommended in the SEO world (Rand seemed to like it, tweeted it, etc.) and it should be useful for this issue.
You also have issues with an expired security certificate, which is returning this error if you try to access HTTPS URLs on the site. Quite a few HTTPS, as opposed to non-secure HTTP URLs, are indexed: http://i.imgur.com/ADX9hBc.png
This should be fixed, and HTTPS URLs should be 301ed to HTTP URLs where the URL does not need to be secure. Here is an example of both versions of the URLs being indexed for the same content: http://i.imgur.com/A7VkACx.png
There is quite a lot of housekeeping to be done on the site to perfect its on-page optimisation, and this will certainly help. There's a chance you are affected by Panda because of this: Google thinks you have duplicated content from the old Shopify blog, and content is duplicated throughout the site in its eyes.
I hope this helps - I know it's a lot of work to clean up the site internally but it's definitely necessary.
Cheers,
Jane