Learn Finnish: Älä raahaa sitä liikaa, tai jalkasi puutuvat. - Don't drag it too much, or your legs will go numb.

Yes, but it changes the phrasing slightly. You could say Älä raahaa sitä sen verran, että jalkasi puutuvat (Don't drag it so much that your legs go numb). The original sentence uses liikaa, tai (too much, or) to express the same consequence as a direct warning.

How do we know jalkasi means "your legs" (plural) rather than "your leg" (singular)?

The verb puutuvat (they go numb) gives it away because it is in the plural form. The nominative plural of jalka is jalat, but when you add a possessive suffix like -si, the plural marker -t drops. As a result, jalkasi can mean either "your leg" or "your legs," and you have to rely on context or the verb to tell them apart.

Why is the object sitä in the partitive case here?

This is a great refresher on object rules. Because this is a negative command (Älä raahaa), the object must be in the partitive case. Even in a positive sentence, raahata (to drag) often takes a partitive object because dragging is usually a continuous, uncompleted action.

Does the verb puutua (to go numb) have a connection to the word puu (tree/wood)?

Yes, it does! The verb puutua literally means "to become wood" or "to turn to wood." It is a very descriptive and memorable way that Finnish expresses the stiff, heavy feeling of a limb falling asleep.