Hello, I am sorry to hear your euonymus is suffering. From your photo it appears its has an infestation of a type of armored scale. I would need additional photos zoomed in on the pest to be sure, but it is most likely euonymus scale, which is both a common and serious pest of evergreen euonymus. There are several methods of treating the infestation, so don't give up hope yet!

Here are my two cents about this pest: if you see beneficial predators, such as ladybird beetles (lady bugs), and the scale numbers are fairly low, I would let nature do its work. You could even go a step further and order the twice-stabbed lady beetles (Chilocorus kuwanae) to release your own predators. 

If you do not see any beneficial predators around, however, you could spray a summer rate of horticultural oil to smother the scale. Horticultural oil is a petroleum based product that is meant to smother soft bodied insects like aphids, scale, mites, young caterpillars, etc. It must make contact with the pest to work as it its not absorbed by the plant. It is also the most gentle to our beneficial insect populations. The directions for dilution, and duration between sprays, will be included in the leaflet label on the bottle. Follow them carefully. It is also advised to avoid spraying horticultural oil on cloudy, humid days above 85 degrees F, as in those conditions the oil will evaporate slowly, possibly resulting in leaf burn.

If the scale infestation is very severe, you could instead cut the euonymus to the ground and treat the new growth and shoots with horticultural oil sprays as needed to prevent re-infestation. That is a drastic measure but sometimes the only option if you wish to save a shrub and the pest population is too great to control with spraying alone. If you opt to do this, adequate mulch and regular watering during dry spells will help prevent winter leaf drop.

I hope this helps, good luck!

You're so welcome!