I suppose you want to clear ONLY a specific upvalue otherwise Unset or Clear would have been fine.
You can use TagUnset.
In[1]:= sq /: area[sq] = s^2;
sq /: circ[sq] = 4 s;
In[2]:= sq /: circ[sq] =.
In[3]:= {area[sq], circ[sq]}
Out[3]= {s^2, circ[sq]}
I found another user try to do something similar here: Clearing OwnValues, DownValues, UpValues and SubValues separately