Is it possible to extract magnesium from epsom salt?
Supposed you are trying to obtain magnesium metal from Epsom salt, $\ce{MgSO4.7 H2O}$:
Is is worth the effort?
Magnesium metal in the form of chips (particle size 4-30 mesh) in decent purity (99.98%) is available from suppliers such as Sigma-Aldrich for about 150 Euro per kilogram.
Can I use electrolysis to generate $\ce{Mg}$ metal?
Yes, but you wouldn't want to do that at home. An older industrial process uses electrolysis of molten magnesium chloride, $\ce{MgCl2}$ (mp. is around 700 °C). While $\ce{Mg}$ metal is formed at the cathode, chlorine gas is released at the graphite anode. Did I mention that this isn't meant to be done at home?
Can I convert $\ce{MgSO4}$ to something more usable to make $\ce{Mg}$ metal?
Yes, in principle. A group of Chinese researchers examined the conversion of  $\ce{MgSO4}$ to  magnesium oxide, $\ce{MgO}$ by heating in the presence of natural gas at temperatures around 500 °C and outlined their results in
Geochemical Journal, 2011, 45, 97-108.
The initial pressure by natural gas at room temperature was 3 MPa, but upon heating to the final temperature, the pressure in the reactor was as high as 12-20 MPa! This can't be done at home and it shouldn't be.
What if I would have $\ce{MgO}$? What could I do with it?
Magnesium oxide, $\ce{MgO}$, is indeed the most important starting material in the production of magnesium metal in the Pidgeon process. Here, magnesium oxide is heated in the presence of silicon in an evacuated reactor. Silicon is oxidized to silicon dioxide, magnesium oxide is reduced to magnesium metal. The latter boils off (bp. around 1100 °C) and is condensed. This isn't kitchen chemistry either.
In summary, you're better off buying some magnesium metal from a supplier of your choice!