The Most Common Smoothie Problems.

The Most Common Smoothie Problems (& How to Solve Them)
Not blended enough.

If your straw is getting clogged with chunks, it may be because you're not adding the ingredients to the blender in the correct order. (Here!)
Alton Brown recommends you add the liquid first, towards the bottom (to get the blade whirring smoothly and quickly).
To the liquids, add leafy greens, then heavier items like chunks of frozen fruit.
Start the blender on low speed, gradually increasing to higher speed, to make sure a vortex forms.

If your greens are still too coarsely chopped for your liking, you can pulverize them with the liquid before adding the other ingredients (or it may be time to invest in a high-speed blender).