Rich mix or clogged muffler are the usual suspects.
Check your fuel mixture first, then the muffler screen.
Smoke from the muffler almost always means the engine is burning too much oil — either because your fuel mix is too rich (for a chainsaw that’s usually 50:1, but check your manual) or because the spark arrestor screen is plugged with carbon and the exhaust can’t escape cleanly. Air leaks or a dirty air filter can also make it run rich, but start with the simple things.
If the smoke is white/blue, it’s burning oil. If it’s dark black, it’s likely a rich fuel mix or restricted exhaust.
Pull the muffler off and inspect the screen. If it’s crusted over, clean it with a wire brush or replace it. If that’s fine, dump the gas and mix a fresh batch at the correct ratio — don’t guess, measure.
I’d also check the bar oil system. If the chainsaw is leaking bar oil onto the muffler, it’ll smoke like crazy. That’s not a combustion issue, but it looks the same.
Don’t let it run smoky for long — you’ll bake carbon into the piston and ruin the saw.