My Yardman riding mower will not pull itself in low speed.?

Presuming you've installed the correct drive belt, then the next thing to check is the transmission adjustment. That should be done by a qualified lawn equipment repair shop. You can do it yourself, but you've got to know what you're doing to do it right.

Are you meaning engine speed or forward motion speed. A small mower engine should always be operated at maximum speed allowing the governor to adjust for torque requirement. Start doing that and your "pull itself" problem goes away and your mower works better and lasts longer. Use the clutch only, never the throttle, to compensate for walking speed. For the next mower, skip the cheap (MTD derivatives) and invest in a walk behind that will automatically adjust the mower speed to your walking pace.

This is a riding mower. The engine runs fine and is not affected. It is just the belt drive transmission that slips.