If you open up Markdown.Editor.js, and scroll to approximately line 1360 (it varies depending upon which version you're using), you'll see an area with:
group1 = makeGroup(1);
buttons.bold = makeButton("wmd-bold-button", "Bold - Ctrl+B", "icon-bold", bindCommand("doBold"), group1);
buttons.italic = makeButton("wmd-italic-button", "Italic - Ctrl+I", "icon-italic", bindCommand("doItalic"), group1);
group2 = makeGroup(2);
buttons.link = makeButton("wmd-link-button", "Link - Ctrl+L", "icon-link", bindCommand(function (chunk, postProcessing) {
return this.doLinkOrImage(chunk, postProcessing, false);
}), group2);
buttons.quote = makeButton("wmd-quote-button", "Blockquote - Ctrl+Q", "icon-blockquote", bindCommand("doBlockquote"), group2);
buttons.code = makeButton("wmd-code-button", "Code Sample - Ctrl+K", "icon-code", bindCommand("doCode"), group2);
buttons.image = makeButton("wmd-image-button", "Image - Ctrl+G", "icon-picture", bindCommand(function (chunk, postProcessing) {
return this.doLinkOrImage(chunk, postProcessing, true);
}), group2);
So on and so forth. Simply quote out the buttons you don't want.
Alternatively, you can simply leave out the entire wmd-buttons div and only use the editor and preview components.