If you still need an answer - and I needed one, which is how I ended up at this page in the first place - Use [[MORE]] in the spot where you want the break to happen. It's a tumblr-specific thing, and it works in both HTML and Markdown mode.
Example:
Lorem ipsum dolor sit amet, consectetur adipiscing elit. [[MORE]] Pellentesque quis lacinia orci, vel fringilla quam. In vitae tortor vitae purus volutpat consequat. Pellentesque sagittis libero vitae hendrerit dignissim. Cras laoreet.
Displays on people's dashboards as:
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Read More →
With the "Read More" linking to the full post, as it would if you had added it in the HTML or WYSIWYG editor:
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Pellentesque quis lacinia orci, vel fringilla quam. In vitae tortor vitae purus volutpat consequat. Pellentesque sagittis libero vitae hendrerit dignissim. Cras laoreet.