There are many examples on MBED for ST7735 controlled LCDs, but they're mostly for the AdaFruit LCD. This is a working example of the library used for the cheap-as-dirt KMR-1.8 SPI 128x160 TFT LCD, on a "Black Pill" STM32F407VE developement board.

Dependencies:   24_TFT_STMNUCLEO mbed

Revision:
0:368cfb35a89a
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main.cpp	Fri Sep 28 03:37:23 2018 +0000
@@ -0,0 +1,37 @@
+// WORKS with KMR-1.8 128x160 TFT LCD
+//
+// Hookup: 
+// VCC, LED+ - 3.3V
+// CS - PC_4
+// SCLK - PA_5
+// SDA - PA_7
+// A0 - PC_5
+// RESET - PA_4
+
+
+#include "mbed.h"
+#include "st7735.h"
+#include "terminus.h"
+  
+ // create the lcd instance
+ // ST7735_LCD( PinName CS, PinName RESET, PinName RS, PinName SCL, PinName SDA, PinName BL = NC, backlight_t blType = Constant, float defaultBackLightLevel = 1.0 );
+ ST7735_LCD lcd( PC_4, PA_4, PC_5, PA_5, PA_7 ); // control pins
+
+ int main()
+ {
+     // initialize display - place it in standard portrait mode and set background to black and
+     lcd.Initialize( LANDSCAPE_REV, RGB16  );   
+     lcd.ClearScreen();
+     // various graphics primitives
+     lcd.DrawPixel(1,1,0xFF9FFF);
+     lcd.DrawLine(10,10,150,10,0xFF29A9);
+     lcd.FillCircle(70,60,10,0x00FF00);
+     lcd.DrawRect(30,80,50,100,0x0000FF); 
+     lcd.DrawRect(60,80,80,100,0xFF00FF);   // any RGB mix XX-XX-XX
+     lcd.DrawRect(90,80,110,100,0x00FFFF);   // any RGB mix XX-XX-XX
+     lcd.DrawRect(120,80,140,100,0xFFFF00);   // any RGB mix XX-XX-XX
+     lcd.SetFont( &TerminusFont );
+     // print something on the screen
+     lcd.Print( "Hello, World!", CENTER, 25 ); // align text to center horizontally and use starndard colors
+     while ( 1 ) { }
+ }