Can l add more gears by replacting the cassette on my mountain bike?

To do that you need to change the shifter and derailleur as well.

Different brands, and different numbers of cogs on the rear require different amounts of pull on the gear cable to shift one gear, and the cogs, chain etc are all different sizes. This also means that the total cable moved to get from highest to lowest gear is generally also different. Note that it's usually specified in tenths of a millimetre (0.1mm), so everything has to be quite precise. Otherwise the bike won't stay in gear.

While you can change everything over like this it's generally more expensive than selling your bike and buying a newer or higher spec one with the new groupset on it. If you can find a damaged bike with the necessary parts intact that's likely to be the only cheap way to make the change.

There's also not a lot to gain by adding a couple of gears. Parts tend to cost more when bought separately, than when on a whole bike, so its your call on the value.

From 8 to 10 speed you probably can use the same rear wheel. There's a small chance that you might go to 11, but that depends on the freewheel part of the hub.

You will need to replace the cassette (more cogs), chain (thinner), derailleur (ratios), and shifter (more clicks).

You should change the inner and outer gear cable at the same time, because they're cheaper than the other parts and why not?

Depending on your bike, you might need to replace bartape or handgrips, there's potential of damaging them while changing shifter.

If your shifter is integrated with your brake lever then you need a replacement integrated lever, or buy a separate brake lever to suit.

You probably don't need new shifter or mech for the front. While the chainrings will be for 8 speed chain, the chainring teeth only see the rollers not the outside. With the slightly narrower 10 speed chain, its more possible to drop the chain between the chainrings. The usual hack is to slightly narrow the Front Mech's cage by squeezing with pliers.

So yes it is possible, but expensive and not that much of an upgrade.

Aside - if your existing cassette/chain is worn out and needs changing anyway, then that's a sunk cost which has to be spent, decreasing the "incremental" cost of the upgrade.