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Suppose some function f[x,y]. I want to expand it in series, like

g[x_,y_] = Series[f[x,y], {y,0,2}]

After that I need to plot the graphic of $g$. But it is impossible because of O[y^2] term in the expression for g.

How to throw out this O[y^2] term?

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For this purpose use Normal,

f[x_, y_] = Exp[x*y]

g[x_, y_] = Normal@Series[f[x, y], {y, 0, 2}]

1 + x y + (x^2 y^2)/2

Plot3D[g[x, y], {x, 0, 2}, {y, 0, 2}]
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