Add ellipses to overflowing text in SVG?

I am not aware of an equivalent CSS class for SVG, but you can use foreignObject to embed HTML in SVG. This gives you access to this functionality and is more flexible in general (e.g. you can do automatic line breaking easily).

See here for a complete example.

This function does not depend on d3:

function textEllipsis(el, text, width) {
  if (typeof el.getSubStringLength !== "undefined") {
    el.textContent = text;
    var len = text.length;
    while (el.getSubStringLength(0, len--) > width) {
        el.textContent = text.slice(0, len) + "...";
    }
  } else if (typeof el.getComputedTextLength !== "undefined") {
    while (el.getComputedTextLength() > width) {
      text = text.slice(0,-1);
      el.textContent = text + "...";
    }
  } else {
    // the last fallback
    while (el.getBBox().width > width) {
      text = text.slice(0,-1);
      // we need to update the textContent to update the boundary width
      el.textContent = text + "...";
    }
  }
}

a wrapper function for overflowing text:

    function wrap() {
        var self = d3.select(this),
            textLength = self.node().getComputedTextLength(),
            text = self.text();
        while (textLength > (width - 2 * padding) && text.length > 0) {
            text = text.slice(0, -1);
            self.text(text + '...');
            textLength = self.node().getComputedTextLength();
        }
    } 

usage:

text.append('tspan').text(function(d) { return d.name; }).each(wrap);