How can I write two separate blockquotes in sequence using markdown?

You can separate blockquotes without html elements by using comment markup <!-- --> with an extra whiteline between the blocks:

> Imagination is more important than knowledge.

<!-- -->
>  Never think of the future. It comes soon enough.

<!-- -->
> Anyone who has never made a mistake has never tried anything new.

Of course you can use any HTML elements you like as well (as noted by @pepoloan):

> Imagination is more important than knowledge.

<div></div>
>  Never think of the future. It comes soon enough.

<div></div>
> Anyone who has never made a mistake has never tried anything new.

An empty header, #, followed by a space also works.

> Hello World

# 

> Goodbye world

Unfortunately it isn't much better than <!-- --> But I kind of like it more, and use it.