I cannot see this functionality in the spec. The HTML output would obviously be <del></del>

Here's a draft of an extension to do that, in the format I've been throwing around:

Extension: Strikethrough

A new inline Markdown element is added, Strikethrough. It follows the same parsing rules as strong emphasis (§6.4), except that the asterisk and underline are replaced by a tilde ~, and the <strong> tag is replaced with the <del> tag.

A double ~~ can open strikethrough iff

1. it is not part of a sequence of 3 or more unescaped ~s, and
   
2. it is not followed by whitespace.

A double ~~ can close strikethrough iff

1. it is not part of a sequence of 3 or more unescaped ~s, and
   
2. it is not preceded by whitespace.

Strikethrough has a precedence equal to emphasis and strong emphasis.

OK. I think ~ is better than - that is used in for instance in JIRA (-some deleted text-) as it is a less common character used in general language.