SPIM adopts the endian-ness of the machine on which it runs. (http://www.dsi.unive.it/~arcb/LAB/spim.htm#Byte%20Order)
Here's a little program to check the endian-ness of your machine:
.data
word: .word 1
bigStr: .asciiz "Big Endian\n"
littleStr: .asciiz "Little Endian\n"
.text
main:
la $t0 word
lb $t1 0($t0)
beqz $t1 bigEndian
littleEndian:
la $a0 littleStr
addi $v0 $zero 4
syscall
jr $ra
bigEndian:
la $a0 bigStr
addi $v0 $zero 4
syscall
jr $ra