解：由题意可知$|m|-2=1$，且$m-3≠0$，解得$m=-3$
$(3\ \mathrm {m^3}-\frac {5}{2}m²-\frac {1}{3}m-2)-(2\ \mathrm {m^3}-\frac {3}{2}m²+\frac {5}{3}m-3)$
$=3\ \mathrm {m^3}-\frac {5}{2}m²-\frac {1}{3}m-2-2\ \mathrm {m^3}+\frac {3}{2}\mathrm {m^2}-\frac {5}{3}m+3$
$=\mathrm {m^3}-\mathrm {m^2}-2m+1$
把$m=-3$代入上式，得原式$=-27-9+6+1=-29$
