ClearAll["Global'*"]

<<Feyncalc`

(*Bhabha scattering/Setting momentum values*)
SP[p1,p1]=SP[p2,p2]=SP[p3,p3]=SP[p4,p4]=m^2
SP[p1,p2]=SP[p3,p4]=s/2-m^2
SP[p1,p3]=SP[p2,p4]=m^2-t/2
SP[p1,p4]=SP[p2,p3]=m^2-u/2

ampa1=GA[μ].(GS[p2]-m).GA[ν].(GS[p1]+m)
ampa2=GA[μ].(GS[p3]+m).GA[ν].(GS[p4]-m)
ampa=(e^4/s^2)Tr[ampa1]Tr[ampa2]//Contract//Simplify

ampb1=GA[μ].(GS[p3]+m).GA[ν].(GS[p1]+m)
ampb2=GA[μ].(GS[p2]-m).GA[ν].(GS[p4]-m)
ampb=(e^4/t^2)Tr[ampb1]Tr[ampb2]//Contract//Simplify

ampab=(2*e^4/(s*t))Tr[GA[μ].(GS[p3]+m).GA[ν].(GS[p1]+m).GA[μ].(GS[p2]-m).GA[ν].(GS[p4]-m)]
Contract[%]//Simplify

ClearAll[m]
amp=ampa+ampb+ampab
Simplify[%]

amp/.m->0//Simplify