There re a a lot of people on this thread that don't understand what mindfulness is.
It's not about clearing your mind, it's not about focusing on your problems, it's not about achieving some sort of meditative calm state, it's not about relaxing, it's not about navel gazing.
It's about being present, being aware of what you are feeling in your mind and your body whatever that is (not trying to change it), and focussing your mind on one thing, it's about getting out of your head and into your present experience. It's an antidote to modern life where our minds are usually full with stuff, and jumping about, often spiralling, and running from one thing to the next thing on the list.
Your focus can be anything. It can be your breathing but it can also be the feel of your feet or your body or the wind on your face or the smell in the air as you are running, or the feeling of the dirt on your hands or the sun on your face, or the beauty of the plants as you are gardening. Mindfulness can be anything. It's about being present the moment rather than thinking about one thing (or usually multiple things at a pace) while doing something else. The latter isn't really very healthy for us but what modern lives tend to push us to do. Being mindful just turns that for a little bit and over time, with practice, trains our minds (and therefore our emotions) to be a bit calmer and a bit more present.
CBT can be very effective with the right therapist (I find the CBT therapists that you get referred to now under the NHS not particularly great tbh but have had fantastic CBT from a clinical psychologist in the past) but like all therapies it doesn't work for everyone and certainly neither mindfulness nor CBT, although they can be helpful and effective, should be viewed as a universal panacea and they shouldn't be the only options on offer.