Save the handles of each plot then delete accordingly.
%Example
figure
hold on
[X,Y] = meshgrid(0:6,0:6);
U = 0.25*X;
V = 0.5*Y;
q=quiver(X,Y,U,V,0,'b');
p=plot(X(:),Y(:),'k-');
f1=fimplicit(@(x,y) x.^2-y.^2-1, 'r--');
f2=fimplicit(@(x,y) x.^2.*sin(x)-y, 'g:');
hold off
%Check how many plots there are on the current axis
ax=gca;
ax.Children
%Delete the 2nd fimplicit plot
delete(f2)
%Updated axis after deletion
ax.Children
You can also get the children of the current axis of the figure (i.e. all the plots (and any text), as I have done above) and delete plots accordingly, but that will be tedious.
