Last year I planted spurge in a container garden. It made it through the winter and is starting to grow again. It is very gangly and top heavy. If I cut it back, will it survive and become bushier?
There are several types of euphorbia. A common type is Euphorbia amygdaloides, which is used as an ornamental ground-cover plant. You did not mention where the plant is growing. It can be gangly and top heavy if grown in the shade and it does not like wet soils and poor drainage. Check this.
The plant does not require a lot of pruning. You can prune out any dead portions now and prune the stems after flowering. You may have to wait and see how the plant looks this growing season.
Broken stems will produce a milky sap that may cause skin irritation in some people. Wear protective gloves and use a shovel to dig out the unwanted plants and their roots. It is poisonous if ingested. Here is more information http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?taxonid=268086&isprofile=0&cv=4
The euphorbia that I have is similar to "Ascot Rainbow." It is in a pot and last summer was planted with some annuals. At this time it is over 2 feet tall and getting new growth. The spot gets a fair bit of sun although it is shady in the late afternoon.
Pinch stems back to 6" in mid-spring immediately after flowering to encourage bushy growth. Wear gloves when working with this plant to avoid suffering harm from the toxic milky plant sap (eye inflammation, temporary blindness, skin rash/burning).
Here is more from Missouri Botanical https://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?taxonid=364042&isprofile=0&