I also came across this problem some time back.
The reason why it happens is that the upper part of the loaf is kept usually fluffy in most of the breads hence causing it to crumble when cut.
The lower side of the bread loaf on the other hand is softer and firmer than it's top.
THE HACK
: Keep the loaf upside down and then cut it.
You can moisten your knife a bit or apply butter for best results.
See this Illustration: It works!
lifehacks.stackexchange.com/users/21925/Swasti Gupta
You can place a cooling rack, or an oven rack, across your kitchen sink.
The loaf goes on top of that while you're cutting slices.
All the crumbs wind up in the sink, which makes them easy to rinse down the drain.
Just be sure to hold onto each slice of bread when it's about to be separated from the loaf so it doesn't fall through the rack!
You could also place the rack across a clean kitchen trash container, so the crumbs fall straight into the trash bag.
(BTW, I saw lumber in my sink too, to catch the sawdust.
I live in an apartment that doesn't have outdoor areas conducive to woodworking.
When sawing lumber, I first add a wet paper towel in the bottom of the sink to catch most of the sawdust.)
lifehacks.stackexchange.com/users/4198/BrettFromLA
Having the best bread knife (or as it is sometimes called, bread saw) helps.
You also have the use it right, making a sawing motion, not pushing it much (or at all.)
It does not need to be an expensive knife, it has to have the right make, with saw like teeth (if flat, not at an angle as saws have.)
In kitchen stores (and some cheaper shops)
you can find two part bread boards, one a dish to catch the crumbs, the other on top open slats of wood, allowing the crumbs to fall through.
When you keep the bottom part clean, you can catch and use the crumbs if you want.
In cooking many people use bread crumbs.
I did an internet image search on -cutting board bread, two parts- and found this one among many others.
Only commercial links, as far as I could see, so no photos here.
lifehacks.stackexchange.com/users/19058/Willeke
One way I found is to wet the knife before starting to cut.
When the knife is wet, there are less crumbs.
Still not ideal, but better than nothing.
lifehacks.stackexchange.com/users/1399/Shadow Wizard is Ear For You
I do that inside a big transparent plastic bag.
Yes, the bread, the cutting board, the knife, both of your hands - put them all deep inside the bag, then cut the bread.
lifehacks.stackexchange.com/users/21176/Headcrab
When I go to the bakery and buy crumb prone bread, I ask them to slice it for me --- problem avoided!
Packed in a plastic bag it remains fresh.
lifehacks.stackexchange.com/users/6982/Alan
When cutting a crispy bread, I usually end up with such a mess: (baguette in this example)   Crumbs all over the place. How can I avoid those crumbs and have a clean cut of the bread?
How to avoid crumbs when cutting a crispy bread?
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lifehacks.stackexchange.com/users/1399/Shadow Wizard is Ear For You
There are a number of ways to avoid this problem but having a good quality knife will definitely help. You could also consider wetting the knife first. You might want to consider cutting the loaf upside down or could even consider cutting the bread over your sink to catch the crumbs. Alternatively, you cout cut the loaf inside a transparent plastic bag or simply ask the bakery to slice it for you when you buy. The options are to cut the loaf upside down and smear butter over the knife or wet it first, cut it on an oven rack placed over your sink, make sure you have the right kind of bread knife, cut it inside a plastic bag or get the baker to cut it for you.
Cut the loaf upside down and smear some butter over the knife or wet it first. Place an oven rack or similar across the sink and put the loaf on the roack to cut. Make sure you have the right kind of bread knife. Wet the knife before cutting. Cut the bread with the breadboard, bread, knife and both your hands in a plastic bag. Ask the baker to cut it for you.