Definitely pluck them, though they will likely get crowded out by the mint once it does get a chance to establish. Until then, it will be best to remove them.
Here is an article that will help you to care for mint:
Would like to know what it looks like
Here's an article with a photo of potted spurge: https://www.gardeningknowhow.com/plant-problems/weeds/spotted-spurge-control.htm
Bought three of theses plants Mediterranean Spurge Swan Plant. Potted in full sun and turned brown, watered every two weeks. Why the browning? Also how do you care for them in winter? They look dead.
This plant, also known as Euphorbia, has some specific growing requirements. Here are articles you can check to see if your plants are receiving what they need: https://www.gardeningknowhow.com/ornamental/cacti-succulents/euphorbia/growing-euphorbia-plants.htm
Deep watering may have allowed the roots to stay wet for too long, or your plants may have contracted a fungus. You may want to prune the bad stems down at the base of the plant, and if you do decide to prune them back, please wear gloves - the sticky substance inside them is toxic.
Does this plant need to be in a dry place. Does it not go in the ground where rain gets at it.
Spurge is also known as Euphorbia. You are in Zone 10 and shouldn't have any problem leaving it in the ground over the winter, but if you want to protect it, you may wrap it lightly in some kind of insulating material. It needs some water, but don't water it from the top and don't let it get soggy, or get completely dry. Also, beware of the sticky substance within the stems - it could cause skin irritation.
I have planted Japanese Spurge under a tree that receives very little sun. My concern is Winter, when all the leaves have dropped and hours of afternoon sun will cover this area. Am I right to be concerned? Thanks for any replies.
The increased sun angle, and decreased daylight hours will be enough to keep it from getting too beat up over winter.
If you find that the sun does scorch the plant, you might try and erect a shade cloth for a portion of the day.
Here is some information on the care of the plant: