The rose in question is a floribunda which usually comes in 'bush' form or 'half standard', in whatever case suckers need to be removed to avoid reversion.
All roses have what is known as 'pinate' leaves, ie a stalk with several leaves coming off of it, in my experience cultivated roses usually have 5 leaves per stalk but suckers often have 7 or more and are usually easily reconised by being a lighter/ brighter green compaired to the rest of the bush.
As Clanad suggests the suckers should be cut back below ground, if this is where they're coming from, draw the soil away with a hoe to determin exactly where the sucker starts from and cut with your secautres as close to the main plant as possible, push back soil and firm down well with your heel. All the best Tbird+