这里有几个错误和假设可能出错。 我只会把注意力集中在那些立即显而易见的东西上。

#include <iostream>
#include <fstream>
#include <string>
using namespace std; // only for demos/slideware/toy projects.
int mindex = -1;
string word[10]; // we will only ever get 10 strings? 
                 // 10 is a magic number use a const like const int maxWords = 10;
                 // using std::array will catch problems like this, std::vector can be used to dynamically resize the array.

void push(string p);
void top();
void pop();
bool isEmpty();

int main() {
    string filename,eli;
    cout << "Please input a file name" << endl;
    cin>>filename;
    ifstream inData;
    inData>>eli; // reading from not open file!!!
    inData.open(filename);
    if (!inData) { 
        cerr<< "Error opening : " << filename << endl;
        return -1;
    };

    while (inData >> eli) {
        if(inData.fail()) {
            break;
        } else 
            push(eli);
    }

    while (!isEmpty()){
         top();
         pop();
    }

    inData.close();
    return 0;
}

void push(string p){
    index++; // did you mean mindex???
    word[mindex] = p; // fatal error if mindex is not at least 0.
}

void pop(){
  mindex--;
}

void top(){
    cout<<word[mindex]<<" ";
}

bool isEmpty(){
    return (mindex<0);
}

检查mindex在/以上10应该在某处做，除非你绝对肯定永远不会有超过10个单词。