On Squarespace, blog post URLs always begin with the Blog Page URL slug, for example, domain/blog-name/post-name. You cannot remove this.
However if you keep the post titles the same when you import them, you can move your blog to Squarespace without losing the original links.
To do this go to Settings > Advanced > URL Mappings then add the following single line of text, where "blog" is the name of your new Blog Page.
/[name] -> /blog/[name] 301
When you save your changes, all imported blog posts can be reached with their original links. For example, domain.com/post-name will automatically send the visitor to domain.com/blog/post-name.
You'll find more information in the Squarespace guide entitled URL redirects.