I see a number of things that might help you improve your program.
li rather than
la to load a constant
As has already been noted, the
la $v0, 10 instruction should actually be
li $v0, 10. It works that way because you're loading the address 10 into
$v0 which has the same effect, but it's a little strange looking.
$zero at the end of the instruction
add $s0, $zero, $v0 is perfectly valid, but it might look a little odd to those experienced with MIPS assembly language. The typical idiom that I've seen is to put the constant at the end, so that instruction would instead read
add $s0, $v0, $zero which does exactly the same thing, but I find it easier to pick out the
$zero at the end rather than in the middle. That's purely a stylistic suggestion, though.
Minimize register use
You don't really need both a counter and a number. What you can do instead is to use the original input number in
$s0 as the counter and decrement instead of incrementing.
Avoid the overhead of subroutine calls
There's nothing wrong with using subroutines, of course, but they add cycles to the program, and for such a small and simple program as this, the call isn't really necessary. Instead, you could put the loop inline.
Prefer to branch at the end of a loop
while... loop in higher level languages does not even execute once if its condition is false. A
do ... while loop executes at least once, which seems to me to be what is desired here. You can then minimize branching so that there is only one conditional branch at the end of the loop.
Use a better algorithm
Carl Friedrich Gauss came up with a clever algorithm as a child. You can read about it and see if you can implement it for even faster code.
Putting it all together
When we apply all but the last suggestion, we get something like this:
Prompt: .asciiz "Enter number to get summation: "
Output: .ascii "Sum of numbers is: "
# Prompt for input
li $v0, 4
la $a0, Prompt
# Read input
li $v0, 5
add $s0, $v0, $zero # s0 used as loop countdown
add $s1, $s1, $zero # s1 used for summation = 0
add $s1, $s1, $s0 # add number to summation
# Begin summation
addi $s0, $s0, -1 # decrement number
bgtz $s0, loop # keep going until 0
li $v0, 4
la $a0, Output
li $v0, 1
add $a0, $s1, $zero
li $v0, 10