I've created a new product.

Product type: Grouped (product with variants)
Product template: Grouped product (with variants)

I've added my specific variants in the "Linked products" section. Everything works fine except it is displaying "This product is sold out" after the product description. Is that normal? Is there a way to suppress this text?

Hello Jon,

Linked products are different than variants used in Grouped Products. In the case of Grouped products, you should assign "Associated products". Tab visible below the "Linked products". If you add at least one associated products, this text will dissapear.