As soon as you get indoors, soak the clothes in cold water. Don't let the stains sit unattended to for even a minute since the longer a stain has to dry/set the harder it will be to remove. This is especially true of blood. NEVER use warm water to soak blood stained clothes in. As a general rule, though I'm not sure it is true of all stains, warm water sets stains and make them really hard to remove so for the soaking, just use cold or lukewarm water to be on the safe side.
Before you put your clothes in the machine, do treat the stains according to what the stain are. There are several great internet resources if you do a little bit of searching around. For example, a quick search for how to remove grass stains comes up with the suggestion of using some water diluted rubbing alcohol on a sponge to blot the stain before washing. In my stain treating basket, there's olive soap, clear eco friendly dishwashing detergent (since the coloured one can stain), baking soda, alcohol and vinegar.
When you do get around to washing the stained clothes, do read the machine instructions if you still have them around (miraculously we do). Because they might give you some good ideas. For instance our machine has different programs for heavily soiled cotton and heavily soiled synthetic materials. Because synthetic materials generally aren't as though and can't take as high temperatures as can cotton. Thus, when washing dirty cotton use a dirty cotton program. Might perhaps be obvious...but it wasn't to me until I actually read the instructions one day. And it does make a difference, especially for whites.
Talking of whites, I find the very best for getting whites white again is letting them hang outdoors for a few days if you have that option. I once forgot my stained white kitchen towels outside before leaving home for a week, during which there was enough rain to flood the cellar between really warm, sunny days. My towels were as white as when I bought them when I came back, but of course needed another washing after the rain. :)
Other than treating stains for what they are, I'm sorry to say, that there are stains that simply will not be removed. Especially grass stains can be very hard. It is not all fun to accept (especially not with new shirts), but...in my opinion, children clothes aren't ruined because they are stained by a bit of mud or grass. It is rather proof of your child being a happy little one, allowed to play and you should be proud of that fact.
p.s. I don't know how warm it is where you live, but around here wellingtons, rain dungarees with rubber straps that go under the boots (to keep the trousers covered) and then a thin rain jacket on top is the go-to playground attire come autumn and muddy/rainy weather even if it is not currently raining. So might work in the mud park too. Just to strip of after playing/put on before and then rinse when you get back home.